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Powder X-ray diffraction analyses revealed all samples consist of major 1212 phase with tetragonal unit cell (space group P4/mmm), and minor 1201 phase and small amount of other impurities. Table 4.1 lists the values of 1212:1201 phase ratio and 1212 lattice parameters for Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´ (x= 0, 0.1, 0.2, 0.3, 0.4, 0.6) samples. The peaks due to the 1201 phase and GeO2 impurity are marked with a * and # respectively. These 1212:1201 phase ratios was calculated from the diffraction intensities of 1212, 1201 and other phases (impurities) by using the equations 3.11 and 3.12. The 1212 vol. % was well above 80 % for x= 0-0.3, whereas for x= 0.4 and 0.6, the percentage dropped to 72 % and 60 % respectively (Table 4.1). The dropped of 1212 vol. % below 70 % was largely due to much higher amount of 1201 phase and presence of GeO2 and other impurities. The XRD data showed a decrease of c-lattice parameter with Ge content increment. But, there is no significant change in the a-lattice parameter. This suggests possible Ge4+ (53 pm) is much smaller than the ionic radius of Cu2+ (73 pm). It is suggested that, the substitution of Ge for Cu can be an effective way to stabilize 1212 phase formation [Shukor & Arulsamy, 2000].
Figures 4.7-4.12 show the electrical resistivity of Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´ (x= 0-0.6). The results show a slight increased in Tc zero was observed for the Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´, x=0.1 sample (100 K) compared to the free Ge compound (98 K). The Tc onset and Tc zero for x= 0.2 and 0.3 samples were observed above 90 K and 80 K respectively. However, for sample x= 0.4 the Tc onset dropped to 66.3 K (Table 4.2). The x=0-0.3 samples (Figs. 4.7-4.10) showed metallic normal state behavior. Further substitution of Ge caused the normal state to change from metallic-semimetallic behavior at x=0.4 (Fig. 4.11) and insulating behavior at x=0.6 (Fig. 4.12). Based on observed Tc onset values and results of XRD of the samples which showed dominant 1212 phase, it is suggested that the 1212 phase is responsible for the observed superconductivity of the x=0-0.3 samples and not the minor 1201 phase as the Tc onset for the latter has been reported to be below 50 K [Sheng et al., 1991]. The decrease in Tc zero for x â‰¥ 0.2 samples can be attributed to the increasing amount of 1201 superconducting phase and GeO2 within the 1212 superconducting matrix, as shown in Table 4.1. It was suggested that the changes in normal state behavior and depression of Tc zero (Table 4.2), with increment of GeO2 (Figs. 4.1-4.6) are related to the reduction of the charge carrier concentration.
Simple valence calculation indicates that Tl0.85Cr0.15Sr2CaCu2O7-Î´ is slightly overdoped with hole carriers and substitution of the higher valence Ge4+ reduced average copper valence in the CuO2 planes and caused hole concentration to decrease [Subramaniam et al., 1998; Shukor & Arulsamy, 2000; Hamid et al., 2004]. The optimum hole concentration was suggested at x= 0.1, as the sample showed highest Tc zero amongst samples. Further substitution of Ge4+ was expected to decrease holes concentration below the optimum concentration and caused Tc zero to drop. However, intriguingly, Table 4.2 showed that at x= 0.2-0.3 samples, the drop in Tc zero was slow and the values are still maintained above 80 K. Thus, the possible reason for this behavior is given in the light of our discussion on the fluctuation induced conductivity and FTIR analyses below.
The Micrographs of Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´ samples are shown in Figures 4.13-4.18. The micrographs were taken at 3000X magnifications of the fractured internal sections of the samples. The micrographs revealed porous microstructure with grains that are of irregular shapes and of around 1-3 Î¼m in sizes. No significant changes in microstructure were observed for x= 0.1-0.4 samples as compared to the microstructure of the x= 0 sample. The micrograph of x= 0.6 sample shows unclear grains morphology.
Investigation on the superconducting fluctuation behavior of Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´ series by excess conductivity analyses using the AL and LD theories were carried out. Figs. 4.19- 4.22 shows the temperature dependence of electrical resistivity with normal state behavior fitted to the linear relation Ï= a+bT for x=0-0.3. The excess conductivity (âˆ†Ïƒ) was determined by observing the deviation of resistivity, Ï(T) from this background resistivity of linearity line. The inset in Figs. 4.19-4.22 show the curves of the temperature dependence of the derivative of resistivity where the peak temperature, Tcp was used to calculate reduced temperature, Îµ. In order to compare experimental data with the AL theory for the fluctuation conductivity, ln (âˆ†Ïƒ/Ïƒ0) versus ln Îµ was plotted in Figs. 4.23-4.26. The figure shows the fluctuation conductivity for all samples covering the mean field regime, -5< ln Îµ <-2. Table 4.3 listed critical exponent, Î»2D, Î»3D, 2D-3D transition temperature, T2D-3D value for Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´. From critical exponent value (Î»), the conducting channel dimension can be determined. For pure samples only 2D conducting channel was observed. As Ge4+ was substituted into the superconducting sample, the transition from 2D to 3D behavior was observed as temperature was reduced. Table 4.4 shows calculated values of Î¾c(0), J and Î³ of all samples for Tl0.85Cr0.15Sr2CaCu2-xGexO7. Substitution of Ge at Tl1212 compound caused Î¾c(0) to decrease from 0.26Å (x= 0.1) to 0.19 Å (x= 0.2), before increasing back to its highest value of 0.29 Å (x= 0.3). The highest value of J was found at x= 0.3 which also recorded the lowest anisotropy, Î³ value (Table 4.4).
The 2D fluctuation behavior that are observed for the un-substituted Tl0.85Cr0.15Sr2CaCu2O7 sample (Fig. 4.23) is in contrast to the excess conductivity analyses of the Ge substitution samples which indicate 2D to 3D transitions in the normal state (Figs. 4.24-4.26) and also from previous reports on Y123 [Sudhakar et al, 1991, Upreti et al., 1996], (Cu, Tl)-based [Nawazish A Khan & Irfan, 2008; Khan & Husnain, 2006; Khan et al, 2003], Cu-substituted Tl1-xCuxSr1.2Yb0.8CaCu2O7-Î´, Tl1-xCuxSr1.6Yb0.4CaCu2O7-Î´ [Huda & Yahya, 2009; Ahmad et al., 2009] and Yb-substituted Tl0.5Pb0.5Sr2-xYbxCaCu2O7-Î´ [Huda et al., 2008] superconductors which showed 2D to 3D transition behaviors. The 2D to 3D transition in the normal state is suggested to be induced by partial substitution of Ge4+ into CuO2 planes. The calculated Î¾c(0) values for Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´ (Table 4.4) are comparable to the lower value in the range of 0.03-0.68 nm reported for double layer Tl-based compounds [Gernot Krabbes et al., 2006, Safa O. Kasap & Peter Capper, 2006]. The small Î¾c(0) values indicate high degree of anisotropy for the Tl1212 samples.
In analyzing the bond lengths of the superconducting samples, the FTIR measurements were carried out. Fig. 4.27 shows results of FTIR absorption measurements of Tl0.85Cr0.15Sr2CaCu2-xGexO7-Î´ (x=0.1, 0.2, 0.3, 0.6) superconductors. For the un-substituted x=0 sample, the apical oxygen mode of the type Cu(2)-O(2)-Cr is peaked around 534cm-1, Cu(2)-O(2)-Tl around 400-480cm-1 and CuO2 planar oxygen mode around 586cm-1. The peak intensity of Cu(2)-O(2)-Cr decreases whereas and that of Cu(2)-O(2)-Tl mode increases with increased Ge substitution. In Ge substituted Tl0.85Cr0.15Sr2Ca1(Cu2-xGex)O7-d (x=0.1, 0.2, 0.3, 0.6) the apical oxygen modes of type Ge/Cu(2)-O(2)-Cr are observed around 556, 549, 553, 553cm-1 and Ge/Cu(2)-O(2)-Tl mode around 472, 470, 473, 471cm-1. The CuO2/GeO2 planar modes are observed around 589, 588, 573, 565cm-1 for Ge-doping of x=0.1, 0.2, 0.3, 0.6. These observations have shown that Ge/Cu(2)-O(2)-Cr apical oxygen mode is hardened compared to the x= 0 sample whereas the Ge/Cu(2)-O(2)-Tl is softened with increased Ge substitution. In addition, the GeO2/CuO2 planar mode is softened in the Ge-substituted samples with higher Ge.
The hardening of Ge/Cu(2)-O(2)-Cr mode and simultaneously softening of Ge/Cu(2)-O(2)-Tl mode (Fig. 4.27) seems to promotes tilting of bonds of the CuO2 planes, which in turn results in the softening of CuO2 planar mode. However, based on the ratio of Tl to Cr in the composition, it is suggested that softening of Ge/Cu(2)-O(2)-Tl mode dominated in these samples. Observation of decrease in peak intensity of Ge/Cu(2)-O(2)-Cr and increase in Ge/Cu(2)-O(2)-Tl intensity with Ge substitution also further enhanced the suggestion (Fig. 4.27). Additionally, softening of the Ge/Cu(2)-O(2)-Tl apical oxygen modes indicates increasing distance between Tl-O and CuO2 planes in conjunction with XRD results which showed decrease in c-axis length with Ge content (Table 4.1), suggest that the CuO2/GeO2 interplanar distance is reduced with Ge substitution. The reduction caused increased CuO2/GeO2 coupling which in turn lead to an increase in the density of carriers and resulted in enhanced Fermi vector, kF (= (3Ï€2N/V)1/3), coherence length along c-axis Î¾c (= Ñ›2kF/2mâˆ†) and also Fermi velocity VF (= Ñ›kF/m) [Tinkham, 1996; Ihara et al., 1999]. This suggestion is supported by the calculation using the Lawrence-Doniach model which revealed the highest superconducting coherence length, Î¾c(0) and interplanar coupling, J at x=0.3 (Table 4.4). The increased coherence length along the c-axis promotes a decrease in anisotropy, Î³ (Table 4.4) which may explain sustainability of superconducting behavior with Tc zero above 80 K at x= 0.2-0.3 mentioned earlier [Ihara et al., 1999; Ihara et al., 2000]. On the other hand, the sharp decrease in Tc zero for x â‰¥ 0.4 is probably due to the much reduced holes concentration as a result of the high concentration of Ge.
5.2 Tl0.85Cr0.15Sr2-yGeyCaCu2O7-Î´ (y= 0.03, 0.05, 0.08, 0.10, 0.15, 0.20, 0.30, and 0.40) Series
Powder X-ray diffraction analyses (Figs. 4.28 - 4.35) revealed all samples consist of major 1212 phase with tetragonal unit cell (space group P4/mmm) accompanied by minor 1201 phase. The 1212:1201 phase ratio and 1212 lattice parameters for all samples are shown in Table 4.5. The 1212 volume generally increased with Ge content up to y= 0.08 and decreased for y>0.08. However, in general, the 1212 volume was above 84 % for y= 0 to y= 0.15, whereas for y= 0.2 and 0.3, the percentage dropped due to the rise of the 1201 phase and other impurities. The c-lattice parameter from the XRD measurements showed decreasing value as Ge content was increased.
Figures 4.36-4.43 showed the electrical resistivity of Tl0.85Cr0.15Sr2-yGeyCaCu2O7-Î´ (y= 0-0.30) samples. The y= 0-0.15 samples showed metallic normal-state behavior with Tc zero above 88 K (Table 4.6) but as Ge content was further increased, Tc zero dropped to below 80 K with the normal-state behavior of the resistivity curve showed semi-metallic behavior at y= 0.20 and insulating behavior at y= 0.30. Based on the observed Tc onset values (Table 4.6) it is suggested that superconductivity of the y= 0-0.3 samples is dominated by the Tl1212 phase and not the minor 1201 phase as Tc onset for the latter has been reported to be below 50 K [Sheng et al., 1991].
The influence of Ge4+ substitution at the Sr-site on carrier concentration is indicated by the transformation of the normal state from metallic (y=0-0.15) to semi-metallic (y=0.2) and to insulator (y=0.3) behavior with Ge4+ content (Table 4.6). The changes point toward gradual shifting of the doping level to an under-doped state. The free Ge compound (Tl0.85Cr0.15)Sr2CaCu2O7 is slightly overdoped with hole carriers [Sheng et al., 1991] and substitution of higher valence Ge4+ to the superconductor sample caused decrease in hole concentration. For Tl1212, the optimum Cu valence was suggested at 2.33 [Shukor & Arulsamy, 2000; Hamid et al, 2004]. Further Ge substitution leads to underdoping and usually degrades Tc [Nkum & Datars, 1992; Khan & Irfan, 2008]. The increase in 1212 volume with Ge for y= 0-0.08 and the decrease for y>0.08 may be related to the optimum Cu valency. As hole concentration approach the optimum Cu valence value, 1212 phase volume increased, but beyond 2.33, 1212 phase volume decreased. However, intriguingly, for y= 0-0.15, not only the normal state behavior remained metallic, Tc zero was maintained above 87 K before gradually suppressed for y> 0.15 (Table 4.6).
The micrographs of Tl0.85Cr0.15Sr2-yGeyCaCu2O7-Î´ samples showed microstructures of randomly oriented plate-like grains of approximately 4-6 Âµm in grain sizes for y= 0.03-0.15 (Figs. 4.44-4.51). This in contrast to the micrographs of y= 0.2 - 0.4 samples which showed non-homogeneous irregular shaped grains morphology. It is interesting to note that the normal state behavior of the y= 0.03-0.15 samples to be metallic as opposed to the y= 0.2 sample which is semimetallic and the y= 0.3 and 0.4 samples which are insulating. Thus, the results indicate some microstructure influences on the superconducting behavior of the samples.
The excess conductivity analyses of Tl0.85Cr0.15Sr2-yGeyCaCu2O7-Î´ series using the AL and LD models were carried out. Figs. 4.52-4.56 show the temperature dependence of electrical resistivity with normal state behavior fitted to the linear relation Ï= Î±+Î²T for samples y= 0-0.15. The excess conductivity (âˆ†Ïƒ) was determined by observing the deviation of resistivity curve, Ï(T) from this fitted of linear line. The inset in Figs. 4.52-4.56 show the curves of the temperature dependence of the derivative of resistivity where the peak temperature, Tcp was used to calculate reduced temperature, Îµ. The graph of ln (âˆ†Ïƒ/Ïƒ0) versus ln Îµ was plotted for samples y= 0-0.15, which showed metallic normal state behavior (Figs. 4.57-4.61). The curves derived from experimental data were then compared against the computed curves based on the AL equation (Eq. 3.15). For the un-substituted sample, the comparison yielded a 2D fluctuation behavior but as Ge4+ substitution was increased a transition from 2D to 3D behavior was observed with reduction in temperature. The highest observed T2D-3D was 99.6 K for y=0.10 (Table 4.7). Interestingly, the substitution of Ge into Tl0.85Cr0.15Sr2-yGeyCaCu2O7-Î´ was able to induce 2D to 3D transition even at very low Ge content of y= 0.03 (Table 4.7). This confirms strong influence of Ge substitution on the superconducting fluctuation behavior, SFB of Tl1212. Previous studies on Tl1-xCuxSr1.2Yb0.8CaCu2O7-Î´ [Huda & Yahya, 2009], Tl1-xCuxSr1.6Yb0.4CaCu2O7-Î´ [Ahmad et al., 2010] and Tl0.5Pb0.5Sr2-xYbxCaCu2O7-Î´ [Huda et al., 2008] also showed the similar influence of elemental substitutions on SFB and 2D to 3D transition.
By using the Lawrence Doniach equations, the values of Î¾c(0), J, Î³ were determined for all samples and tabulated in Table 4.8. The values of Î¾c(0) for y=0.08 showed the largest coherence length of 0.47 Å amongst the samples. The y= 0.08 sample also showed the highest value of J (0.087) and the lowest value of anisotropy, Î³. The results indicate that Ge substitution can induce modify Î¾c(0) which in turn increase interlayer coupling strength and reduce anisotropy of the sample. The calculated values of Î¾c using the Lawrence Doniach theory, in the present work (Table 4.8), are comparable with the reported Î¾c of double layer Tl-based compound which was in the range of 0.3-6.8 Å [Gernot Krabbes et al., 2006, Safa O. Kasap & Peter Capper, 2006].
FTIR result for Tl0.85Cr0.15(Sr2-yGey)CaCu2O7 is shown in Figure 4.62. In the un-doped Tl0.85Cr0.15Sr2CaCu2O7 (free Ge) sample, the apical oxygen modes in the form of broad bands of types Cu(2)-O(2)-Tl and Cu(2)-O(2)-Tl/Cr are observed between 400-550cm-1 [Ahmad et al, 2010; Kulkarni et al, 1990; Khan & Husnain, 2006]. A broad Cu(2)-O(2)-Tl mode is observed in the wave number range 420-480cm-1 [Ahmad et al, 2010; Kulkarni et al, 1990; Khan & Husnain, 2006] which slightly increases in intensity with increased Ge doping. The Cu(2)-O(2)-Cr/Tl mode [Ahmad et al, 2010; Kulkarni et al, 1990; Khan & Husnain, 2006], however, is softened with increased Ge doping and is observed around 552, 552, 552, 549.3, 548.2, 548, 548, 548cm-1 in Tl0.85Cr0.15(Sr2-yGey)CaCu2O7 (y=0.05, 0.08, 0.10, 0.15, 0.20, 0.30, 0.40) samples. In Tl0.85Cr0.15(Sr2-yGey)CaCu2O7 samples doped with small Ge concentration (y=0.03), the CuO2 planar oxygen mode is observed around 571cm-1 [Ahmad et al, 2010; Kulkarni et al, 1990; Khan & Husnain, 2006]. This mode in Tl0.85Cr0.15(Sr2-yGey)CaCu2O7 (y=0.05, 0.08, 0.10, 0.15, 0.20, 0.30, 0.40) samples is observed around 571, 573, 573.6, 573.6, 573.6, 578.4, 581.6cm-1, Fig.4.62.
The hardening of planar oxygen modes with increased Ge doping is most likely due to electronegativity of Ge. The electronegativity of Ge (1.8 Pauling) is much higher than that of Sr atoms (1.0 Pauling). It is possible that the doped Ge+4 atoms with higher electronegativity and smaller ionic radius would exert more attractive interaction of the apical oxygen atom to Ge atoms which will enhance their bending towards them. The bending of apical oxygen atoms towards Ge+4 atoms would reduce attractive interaction between Ge+4 and CuO2 planar oxygen atoms and consequently would decrease planar bending/tilting which possibly results into hardening of CuO2 planar oxygen with increased Ge doping. In addition, the bending of apical oxygen modes toward Ge resulted in softening of these apical oxygen modes. However, XRD results which showed decrease in c-axis length (Table 4.5) as a result of Ge substitution, indicates possible decrease in separation distance between CuO2 planes. The decrease separation distance between planes would result in increase in density of charge carrier (N/V) and thus imply increase in Fermi vector, kF (= (3Ï€2N/V)1/3) and c-axis coherence length, Î¾c (= Ñ›2kF/2mâˆ†) [Tinkham, 1996; Ihara et al, 1999]. The enhancement of CuO2 planes coupling is suggested to enhance superconducting properties of the compounds and sustenance of Tc zero above 89 K (Table 4.6) for x= 0.03-0.15 [Tinkham, 1996; Ihara et al, 1999].