Phase Formation and Conductivity Fluctuation Investigation in Nanoparticle SnO₂-Added Y₃Ba₅Cu₈O_18 ± δ Polycrystalline Superconductor

Abstract

The influence of 0, 0.20, 0.40, 0.50, and 0.60 wt % nano-sized tin oxide (SnO₂) particles on electrical conductivity fluctuation in normal and superconducting state of the Y₃Ba₅Cu₈O_18 ± δ (denoted as Y‑358) polycrystalline samples is studied. Phase formation and microstructures have been systematically examined. By increasing the content of SnO₂ in YBCO matrix, X-ray diffraction technique showed slight variation in lattice parameters and overall reduction in the orthorhombicity. Scanning electron microscopy observations and the crystallite size calculation also revealed that the grain size and the average crystallite size decreased compared to the SnO₂-free sample. Aslamazov–Larkin and Lawrence–Doniach prototypes were used to analyze conductivity fluctuations based on the electrical resistivity ρ(T) measurements. Superconducting transition temperatures T_C and T_LD have been reported. The influence of SnO₂ addition on the superconducting properties indicates that with the addition of SnO₂ nanoparticles into Y-358 compound, some parameters values such as zero-resistance critical temperature T_C zero, coherence distance alongside the c axis at 0 K ξ_c(0), and super-layer length d decrease in total, while anisotropy γ, critical magnetic fields B_c1(0), B_c2(0), and critical current density J_c(0) increase in SnO₂-added Y-358 specimens compared to the pure one. The reasons corresponding to these scenarios are discussed in details.

1 INTRODUCTION

Thermal fluctuations have been detected in all low-temperature superconductors (LTSCs) and high-temperature superconductors (HTSCs). Investigation on HTSCs concerning the fluctuation phenomena leads to a significant understanding of dynamic mechanism in these materials. Thermal fluctuation is responsible for establishment of superconductivity by Cooper pairs beyond T_C which is commenced about 2T_C. Increasing the Cooper pairs number occurs promptly at the cost of the ordinary electrons which creates fluctuation conductivity throughout the carriers transportation [1, 2]. The analysis of fluctuation-induced electrical conductivity traces to three different influences, so-called the density of states (DoS) and the Aslamazov–Larkin (AL) and Maki–Thompson (MT) expressions. The first term is associated with the reordering of the positions nearby the Fermi energy; meanwhile, electrons involved in pair transportation are inaccessible for a solitary charge transport. In the next one, the creation of Cooper pair results in an equivalent superconducting passage in the non-superconducting stage; lastly, the third expression considers the articulate dispersion of contaminations of the interrelating electrons. Very close to the T_C, the differing performance of the DoS expression is cut off by the MT correction that has opposite sign, while the AL and MT expressions both hint to an improvement of the conductivity above T_C [3].

Superconductor properties can be improved by adding some variety of impurities with nano-size particles. These noticeable improvements are being detectable in YBCO family compounds when they mix with Mn₃O₄, Y₂Cu₂O₅, and Ag nanoparticles [4–6]. However, manipulating and controlling superconductors with nano-sized doping might result in unanticipated modifications of the behavior of these materials [7].

Specific impurities such as tin and tin oxide are often presented partial to YBCO slim layers made up by metallic deposition procedure. These resources construct Sn-based nanoparticles in the superconductors system that can show by way of actual pinning regions [8–10]. Constant spread of tin-founded responded phase was similarly detected while adding tin-oxide into melt texture growth polycrystalline Y₁Ba₂Cu₃O_7 – δ (noted MTG Y-123) [11]. The most recent research in the micro-organization and characteristics of Y123 superconductors manufactured through the thermal behavior technique and by the addition of x = 0, 0.4, 0.8, and 1.0 wt % SnO₂ nano-sized particles showed that the compound with x = 0.4 SnO₂ inclusion demonstrated the greatest superconducting parameters amongst the specimens [12].

In this research for the first time after the similar impetus as earlier research, attempts have been made to investigate the essential evaluation consistent with  varied amount of x = 0–0.60 wt % SnO₂ nanoparticles (35–55 nm) inclusions additional to the Y₃Ba₅Cu₈O_18 ± δ superconductor samples that are fabricated by conventional solid-state response process. For determination of specific inconsistencies in doped and pure composites Aslamazov–Larkin (AL) concept and Lawerence–Doniach (LD) theory were appropriate tools to examine the performance of thermal instabilities conductivity beyond the T_C. We found T_LD, ξ_c(0), and d that are, respectively, boundary temperature at the transition from three-dimensional to two-dimensional, the coherence length alongside the c-axis when the temperature approaches 0 K, and effectual super layer length associated with the two-dimensional classification. Soon after computing the anisotropy γ and the interlayer pairing J, related to our superconductors, also at the zero-temperature condition and the critical current density, thermodynamic, the lower and the upper critical magnetic fields labeled J_c(0), B_c(0), B_c1(0), and B_c2(0) were calculated correspondingly.

2 EXPERIMENTATION DETAILS

Nanopowder of tin oxide with chemical formula SnO₂, purity level 99.7%, and nano-size 35–55 nm was prepared from US Research Nanomaterials, Inc. located in Houston, TX, USA. The tin-oxide nanoparticles have been produced from clean chemical substance and rinsed by purified water. Transmission electron microscopy (TEM) has shown its morphology shape is spherical, with true density of 6.95 g/cm³, the average particle size (APS) of 35–55 nm, with white colour and purity better than 99.5%. Doped samples with SnO₂ nanoparticles and pure Y₃Ba₅Cu₈O_18 ± δ were prepared by conservative solid-state response technique. The powders through chemical formulation CuO, Ba₂CO₃, and Y₂O₃ with high quality and 99.9% purity (Merck, Germany) were used to manufacture YBCO polycrystalline and mixed at a ratio of Y : Ba : Cu = 3 : 5 : 8. The hard-pressed pellets were made of the assorted materials and subsequently underwent calcination cycle during 12 h at 900°C. This procedure was repeated once more with medium grinding. During the final processing stage, SnO₂ nano-sized elements were added to the foundation powders of Y-358 by crushing and mixing in an agate mortar. The added quantity of SnO₂ was assorted from x = 0 to 0.60 wt % of the entire amount of the specimen. The pressure applied to the mixture grinds in pellets was about 200 bar to form round disks with dimensions of 30 × 4 mm. The samples were enclosed to quartz crystal pipe, and the sintering process was performed at 950°C with 48-h duration in the vicinity of flowing oxygen, with consequently tranquiling to 25°C at a rate of 4°C/min. After preparing pure Y-358 samples and doped with SnO₂ nanoparticles inclusion, X-ray diffraction (XRD), scanning electron microscope (SEM), and resistivity measurements were investigated to evaluate the phase formation, lattice parameters, the oxygen content, microstructures, and conductivity fluctuations. More details about these issues can be found in [6]. Segmentation techniques are used and followed by generating a binary image to exhibit SEM images at more clarity. In fact, by segmenting an image each pixel can only have one of two values to indicate whether it is part of an object or not. The conventional method to generate a binary image is the thresholding fashion in which image pixels intensity is identified below (min) or above (max) particular threshold values so that only pixels falling within a specified range are detected. Therefore, those of pixels intensity values above the threshold pointed to a foreground (desirable objects) whereas all the remaining values contributed to a background.

3 EXCESS CONDUCTIVITY STUDY

Aslamazov–Larkin (AL) concept [13] that describes the conductivity fluctuation beyond critical temperature is used by the following formula:

$$\Delta \sigma = A{{\varepsilon }^{{ - \nu }}}.$$

(1)

Here, A and ν are named AL constant and Gaussian analytical exponent, respectively. The latter is reliant on the dimensionality of superconducting scheme while ε symbolizes the reduced temperature as follows:

$$\varepsilon = \ln \left( {\frac{T}{{T_{{\text{c}}}^{\rho }}}} \right).$$

(2)

According to the Gauss–Ginzburg–Landau (GGL) approach, ε $\ll$ 1 and by means of the following approximation for the reduced temperature, frequently used in the Aslamazov–Larkin theory

$$\varepsilon = \ln (T{\text{/}}T_{{\text{c}}}^{{\text{P}}}) \cong (T - T_{{\text{c}}}^{{\text{P}}}){\text{/}}T_{{\text{c}}}^{{\text{P}}},$$

(3)

where $T_{{\text{c}}}^{{\text{P}}}$ is the temperature correlated to the peak obtained from dρ/dT.

Pertinent to the AL model [13] and in the mean-field area by deducting the backdrop normal-stately conductivity from the self-possessed conductivity, the fluctuation-induced conductivity Δσ is generally expressed as follows [14]:

$$\Delta \sigma = {{\sigma }_{{\text{m}}}}(T) - {{\sigma }_{{\text{n}}}}(T),$$

(4)

where σ_m(T) and σ_n(T) categorize the measured and normal conductivity, respectively, which is extrapolated above 2T_C. σ_n(T) is computed in the presumption of a linearized or a Zou–Anderson requirement for conductivity σ(T) = 1/ρ(T). The following equation demonstrates relationship between D the dimensionality arrangement and ν the Gaussian analytical exponent,

$$D = 2(2 - \nu ).$$

(5)

The Gaussian critical exponent ν which is a parameter dependent on D, designates with double parts:

(1) For 3D part associated with ν = –0.5 and A = A_3D we can write:

$$\Delta \sigma = {{A}_{{3{\text{D}}}}}{{\varepsilon }^{{ - 0.5}}},$$

(6)

where A_3D = $\frac{{{{e}^{2}}}}{{32\hbar {{\xi }_{{\text{c}}}}(0)}}$ and ξ_c(0) shows coherence length in c direction of multilayer structure at 0 K.

(2) For 2D contribution when ν = –1 and A = A_2D, then the excess conductivity can be written as

$$\Delta \sigma = {{A}_{{2{\text{D}}}}}{{\varepsilon }^{{ - 1}}},$$

(7)

where A_2D = $\frac{{{{e}^{2}}}}{{16\hbar d}}$ and d is the periodicity length of superconducting layers. These effective ν values for 3D and 2D contribution defined paraconductivity fluctuation [15]. However, the graphs of ln(Δσ) versus ln(ε) for none-added and doped Y-358 accomplish resolution of the explainer values. These values can be obtained from the slopes of linear fitting to link investigational numbers with theoretically expected data. In Gaussian fluctuations region if the plots consist of three distinct regimes, another contribution may be introduced as follows:

(3) For 1D contribution associated with ν = –1.5 and A = A_1D, we can write:

$$\Delta \sigma = {{A}_{{1{\text{D}}}}}{{\varepsilon }^{{ - 1.5}}},$$

(8)

where A_1D = $\frac{{{{e}^{2}}{{\xi }_{{\text{c}}}}(0)}}{{32\hbar \omega }}$ and ω is the wire cross-sectional zone related to the 1D scheme. According to layered superconductors and Lawrence–Doniach context [16], the analysis of the fluctuation conductivity above the mean critical transition temperature $T_{{\text{C}}}^{{\text{P}}}$ were pe-rformed because the excess conductivity occurs in the layers of superconductors joined by Josephson tunneling

$$\Delta \sigma = A\frac{{\sqrt {\varepsilon (\varepsilon + J)} }}{{\varepsilon (\varepsilon + J)}}.$$

(9)

A_2D = $\frac{{{{e}^{2}}}}{{16\hbar d}}$ is named the temperature-independent amplitude while J is named the coupler among the superconductors layers which is constant and defi-ned by

$$J = {{\left( {\frac{{2{{\xi }_{{\text{c}}}}(0)}}{d}} \right)}^{2}}.$$

(10)

Here, ξ_c(0) is the coherence length alongside c-axis at 0 K and d is defined as the interlayer placing. In weak-link situation when J $\ll$ 1, Eq. (9) decreases to the 2D expression. The 3D term is obtained in the condition J $\gg$ 1. For YBCO specimens, the Lawrence–Doniach principle [17] was used to find the ξ_c(0) at the changeover temperature, T_3D–2D:

$${{T}_{{2{\text{D}} - 3{\text{D}}}}} = T_{{\text{c}}}^{{\text{P}}}(1 + J).$$

(11)

The anisotropy γ related to layered superconductor classifications was specified by way of [18]:

$$\gamma = \frac{{{{\xi }_{{ab}}}(0)}}{{{{\xi }_{{\text{c}}}}(0)}},$$

(12)

where ξ_ab(0) is the consistency distance in the direction perpendicular to c axis with its value between 10 and 20 Å associated with YBCO [17]. The Ginzburg number can be determined experimentally as

$${{N}_{{\text{G}}}}\, = \,\left| {\frac{{{{T}_{{\text{G}}}} - {{T}_{{\text{C}}}}}}{{{{T}_{{\text{G}}}}}}} \right|\, = \,\frac{1}{2}{{\left( {\frac{{{{k}_{{\text{B}}}}{{T}_{{\text{C}}}}\gamma }}{{B_{{\text{c}}}^{2}(0)\xi _{{\text{c}}}^{3}(0)}}} \right)}^{2}}\, = \,\frac{1}{2}{{\left( {\frac{{{{k}_{{\text{B}}}}}}{{B_{{\text{c}}}^{2}{{\gamma }^{2}}\xi _{{\text{c}}}^{3}(0)}}} \right)}^{2}},$$

(13)

where T_G, T_C, and k_B are the temperature due to ending three dimensionality system, critical temperature, and the constant of Boltzmann, respectively. However, the critical field at zero temperature B_c(0) can be assessed as follows:

$${{B}_{{\text{c}}}}(0) = \frac{{{{\varphi }_{0}}}}{{\sqrt {8\pi \lambda (0){{\xi }_{{\text{C}}}}(0)} }}.$$

(14)

In this equation, φ₀ and λ₀ are called fluxion and penetration depth, correspondingly. The lower and upper critical magnetic fields B_c1(0) and B_c2(0) accompanied with critical current density J_c(0) are computed by implementation the value of B_c(0) and λ₀ into the GL equations:

$${{B}_{{{\text{c}}1}}} = \frac{{{{B}_{{\text{c}}}}\ln k}}{{\sqrt 2 k}},$$

(15)

$${{B}_{{{\text{c}}2}}} = \kappa {{B}_{{\text{C}}}}\sqrt 2 ,$$

(16)

where k is proportion of λ to ξ and entitled the Ginzburg–Landau parameter and eventually J_c is computed as follows:

$${{J}_{{\text{c}}}} = \frac{{4\kappa {{B}_{{{\text{c}}1}}}}}{{3\ln \kappa \sqrt {3\lambda } }}.$$

(17)

4 RESULTS AND DISCUSSION

The X-ray diffraction graphs associated with none-added specimens Y-358 and doped through varied quantities of x = 0–0.060 wt % SnO₂ nanoparticles accompanied with the pure SnO₂ nanopowder are illustrated in Fig. 1.

Fig. 1.

XRD graphs of the powder’s specimens due to untainted Y-358 and doped SnO₂ nano-sized inclusions. The character (•) represents Y-211 as subordinate phases.

The XRD analysis of the samples show that their space group symmetry and structure phase are Pmm2 and orthorhombic, respectively. From X-ray designs, 20 diffraction peaks are obvious along 2θ axis co-rresponding to crystalline flat surfaces of Y₃Ba₅Cu₈O_18 ± δ. Most of the peak positions are in a good agreement with Y-358 [19]. Cumulative effect of the SnO₂ inclusion on the growth of crests implies that the higher SnO₂ doping results in better granules. This influence can be seen apparently about the peak at 32.63° particularly with x = 0.50 and 0.60 wt %, which enunciates the same discussion with other literature [20]. More peaks also exist in the pattern within 29° to 46°, matching Y-211 phase related to the samples. According to SnO₂ nanoparticles, the peaks are linked to (110), (101), (200), (211), (220), (310), and (301) (Miller’s Indexes). These indexes corroborate that SnO₂ nanoparticles with tetragonal structure, and lattice parameters of a = 4.73820 Å, b = 4.73820 Å, and c = 3.18710 Å are harmonized by JCPDS card no. 41-1445. Scherrer equation [21] was used to calculate the average crystallite size Z:

$$Z = \frac{{C{{\lambda }_{{{\text{Cu}}}}}}}{{L\cos \theta }},$$

(18)

where C is defined as form factor excluding any dimension (~0.89), λ_Cu has presented the wavelength of X-ray radiation with the value ~0.15418 nm, L is the line full width at half-maximum in radian and θ is Bragg angle at the peaks. Five peaks at 2θ values of 22.8349567°, 32.58549785°, 32.82142855°, 38.538961°, and 46.6619048° were chosen to obtain the crystallite size. The average crystallite size was found to be 50.32623, 44.65428, 46.63808, 51.63545, and 48.48951 nm, for x = 0, 0.20, 0.40, 0.50, and 0.60, respectively.

There are no substantial modifications related to the X-ray diffraction patterns with adding SnO₂, excepting on behalf of very tiny peaks at 51.8°, and it is hardly to say these peaks can be associated with SnO₂ addition, because they may be overlapped with the base peaks of Y-358 in X-ray diffraction patterns. According to Y-123, some works found extra small peaks associated with the addition of SnO₂ nanoparticles (e.g. [12]). These peaks can be allocated to Ba-SnO₂ related to Y-123 [10, 22], while other indicates belong to Y–Ba–Sn–O [9]. However, our results show that adding a small quantity of SnO₂ within the specimen does not noticeable affect the last outcome into the XRD determination and obviously, in the X-ray curving designs lack of any peak consistent with the Sn-based mixes is evident.

Figure 2 shows so-called lattice parameters a, b, and c for pure and SnO₂ nanoparticles doped samples listed in Table 1.

Fig. 2.

Variant of unit cell dimensions a, b, and c related to Y-358 specimens doped by different quantities of SnO₂ nanoparticles.

Table 1. Lattice constants of Y-358 specimens by various quantities of SnO₂ nano-sized inclusion

Materials analysis using diffraction (MAUD) software based on the Rietveld refinements was used to determine the lattice parameters. Values of a, b, and c related to the non-doped specimen are 3.8245595, 3.8955772, and 31.128101 Å, correspondingly. These data for Y-358 are in agreement with reported before [23–26]; whereas c agrees with others [27, 28]. However, comparing Y-358 to Y-123 regarding a and b parameters shows that the similarity is apparent [27] but in the case of c parameter, for Y-123 it is nearly one third of Y-358 [27, 29]. Adding SnO₂ falls out in an almost constant parameters a and b but a growth in c with doping increase up to x = 0.50. The higher c parameter might stand trustworthy for a poorer interlayer junction and so would be liable for worse qualities of superconductors [30]. The last doping x = 0.60 causes sudden decrease of c parameter. Doping level of some elements such as Co and Fe performs differently when inserted into the YBCO samples: for low-level doping, they are mainly detected at the Cu(I) location and for high-level, they settle at the Cu(II) position [31, 32]. Our results show that the c lattice parameter discrepancies is less than 0.15% while a and b are almost constant by the addition of SnO₂ nanoparticles. However, by inclusion the low doping level (up to x = 0.60 wt %) of SnO₂ nanoparticles, unimportant modifications related to a, b, and c happened, causing that tin did not unify with crystal structure, but instead most probably contributed into the shape of tin-based subordinate phases.

This is an adequate signal that the replacement of tin is not traceable in the Y-358 structure which is supported by other literatures associated with the Y-123 system [12, 33, 34].

Volume of cells obtained by multiplication of unit cell dimensions (abc) accompanied with the average crystallite size and also calculated density for all composites (x = 0 to 0.60 wt %) are recorded in Table 1.

The calculated densities of Y₃Ba₅Cu₈O_18 ± δ specimens with SnO₂ nanoparticles doping (x = 0, 0.20, 0.40, 0.50, and 0.60 wt %) are 4.39426, 4.7794, 4.61165, 4.17922, and 4.62057 g/cm³, respectively. The data indicate that as compared with SnO₂-free sample, by increasing nano-SnO₂ inclusions, the density of YBCO samples increase (x = 0.50 wt % is exceptional), and this progression is involved in an association concerning estimated density and the total of passageway in superconductors so that these aspects increase together with raising nano-sized inclusion, which can be approved by other research [35]. Orthorhombicity Y = (b – a)/(b + a) and oxygen content of the Y-358 phase are depicted in Fig. 3.

Fig. 3.

The orthorhombic distortion Y and oxygen content for Y-358 compounds mixed through different weight of SnO₂ nanoparticles.

The oxygen contents are estimated to be 17.68744, 17.69783, 17.71806, 17.72486, and 17.67508 belonging to add-free and tin-oxide doped specimens associated with assorted impurities (x = 0 to 0.60) Y₃Ba₅Cu₈O_18 ± δ + x wt % SnO₂, correspondingly, and are also placed in Table 1. According to Fig. 3, the differentiation concerning a and b declines through adding SnO₂ nanoparticles up to 0.50 wt % that can be interpreted as the decrease in orthorhombicity regarding the pure composite with higher orthorhombicity, which has been similarly reported in other paper for Ag-doped samples [36].

From 0.20 to 0.50 wt % SnO₂ doping, the values of orthorhombicity decrease while the oxygen content increased in all cases except for x = 0.60 wt % sample. Meanwhile, with nanoparticles dispersed throughout the sample, the orthorhombicity Y is related to oxygen content and reduces by rising SnO₂ doping. Although, our results indicated that increasing tin oxide nanoparticles doping triggered upsurge of the oxygen substance, the properties of high temperature superconductors, particularly YBCO family, are correlated to the O element, the arrangement of O atoms, and their opening situations in the copper–oxygen plane.

Figure 4 illustrates the electrical resistivity measurement for none-added Y₃Ba₅Cu₈O_18 ± δ polycrystalline superconductor and SnO₂ nano-sized addition to Y-358 specimens.

Fig. 4.

Plots of resistivity against temperature of the polycrystalline Y-358 + x wt % SnO₂ nanoparticle doped (x = 0, 0.20, 0.40, 0.50, and 0.60) samples. Inset: Specific section of the graph exhibiting accurate T_co and T_C.

According to this diagram, the general types of the resistivity versus temperature graph are exhibiting metallic behavior in the non-superconducting state and can be formulated as ρ_n(T) = ρ₀ + βT.

In this linear equation, ρ₀ and β are the residual resistivity and the slope of line in the normal state, respectively, where the first term indicates the sample uniformity and the second term represents the essential electronic relationship. The primary decline of resistivity in the transition area is categorized as T_C onset and shown in Fig. 4. This value is 94.20 K for pure sample, which is 1.5 K higher than the data reported in [37]. Other values are 95.95, 96.41, 96.46, and 95.91 K, from resistivity for samples with SnO₂ nanoparticles addition x = 0.20, 0.40, 0.50, and 0.60 wt %, respectively. These numbers rise when SnO₂ doping upsurge up to x = 0.50 wt %. The T_c onset enhancement is well-defined for SnO₂-doped (x = 0.50 wt %) sample which is documented within the inset of Fig. 4 and Table 2.

Table 2. Transition temperature, ρ₀, ρ_n, and β related to resistivity experimentations for Y-358 specimens with varied quantities of SnO₂ nano-sized insertion

This behavior is similar when 0.20 wt % quantities of SnO₂ nanoparticles is added to the Y-123 polycrystalline superconductors [12]. Superconducting transition width T_C, which is listed in Table 2, estimated by the dρ/dT patterns at full width on half-maximum of the peaks, was about 0.405333 K related to pure Y-358 sample and less than 1 K for samples with SnO₂ addition, indicating a good quality of samples. Increasing the value of ΔT_C by adding of SnO₂ revealed that the grains links depressed [38]. This can be ascribed to oxygen possession of granules in the compound being less uniform due to adding of SnO₂ nanoparticles in YBCO samples as compared to the pure one [39]. There is general consensus in the literature that dimensionality of fluctuation conductivity and the critical and mean-field systems are significantly influenced by non-uniformities and types of superconducting granule [19, 40, 41]. Some of the resistivity is two times larger than that reported for ab-plane resistivity of high-purity single crystal Y-123 with the optimum oxygen content at T_C = 92 K [42]. The non-superconducting state resistivity decreases with increasing SnO₂ concentration in all samples except for x = 0.4 wt %. To describe this decrease it is expected that dissimilar crystallographic alignments and consequently granule border-lines, which influence the electron scattering deficiency factor, are responsible for reduction of resistivity. In non-superconducting state, resistivity is correlated to absorbency, granule border spreading, and its linearity during a slower temperature intermission corroborates the information that the formulation and manufacture of the compounds are completed properly, for pure and SnO₂-doped YBCO samples.

According to Fig. 4 and its inset, it can be seen that only for sample x = 0.40, the electrical resistivity increases as compared with the pure one and for the other samples decrease.

Data related to this matter, ρ₀(0 K) and ρ_n(290 K), versus Y-358 + x wt % SnO₂ addition are listed in Table 2.

These outcomes denoted that the entire specimens change to superconductivity state below 85 K. The occurrence of lower resistivity with SnO₂ nanoparticles addition in normal state can be clarified by the equality in the transporter attention because of the oxygen doping balanced and rising the relaxation time due to a less quantity of imperfections, disarray, and non-uniformities whilst the SnO₂ doped upsurges. Figure 5 displays the differentiation of resistivity dρ/dT graph which has been functioned for the calculation of the critical superconducting temperature T_C.

Fig. 5.

The differentiation of resistivity conspiracies against temperature of Y-358 specimens mixture with varied amounts of SnO₂ doping.

The temperature corresponding to the peak of this curve defines the critical superconducting temperature $T_{{\text{C}}}^{{\text{P}}}$ and is recorded in Table 2. While inclusion of SnO₂ dopant rises up to x = 0.50, the critical temperature ($T_{{\text{C}}}^{{\text{P}}}$) is enhanced and suggesting intragranular variations related to the assimilation of tin. The upsurge of T_C for Y-358 with 0.50 wt % SnO₂ nanoparticles inclusion specimen is the biggest value in this research and x = 0.60 causes the reduction of T_C to the 95.088 K. However, related to this matter the case of x = 0.50 is the optimum value for the critical temperature. Whenever T_c of 0.20 wt % SnO₂-added sample reached 94.91378 K, it could be compared with the T_C of 0.40 wt % SnO₂ nano-sized inclusion specimen and approached nil resistivity by the T_C zero equivalent to 85.15309 K. This investigation designates that with SnO₂ doped up to 0.50 wt %, the T_c of prepared specimens will increase to 95.35822 K ultimately so denoted in Fig. 5 accompanied by a middling of ~0.75 K transition widths.

Figure 6 illustrates a plot of ln(Δσ) against ln(ε) for pure and nano-size SnO₂-doped Y-358 specimens.

Fig. 6.

Graph of ln(Δσ) against ln(ε) of the Y-358 + x wt % SnO₂ nanoparticles addition (x = 0, 0.20, 0.40, 0.50, and 0.60) specimens. The dense streaks illustrate ν_cr (–0.32547 ≤ ν_cr ≤ –0.24502 for critical region), the theoretical slopes –0.5, –1, –1.5, and –3 on behalf of 3D, 2D, 1D, and SW schemes, respectively. Critical, mean-field, and short-wave regions are denoted by CR, MFR, and SWR symbols, respectively.

This figure aims to associate the experimental data related to conductivity fluctuation Δσ with the theoretic calculations of excess conductivity. To that effect, every curve exhibited in Fig. 6a might be clearly partitioned into three separate areas, namely, critical fluctuation, Gaussian or mean-field fluctuations, and short-wave fluctuation areas. Critical fluctuation system coupled by ν_cr = –0.24502 related to pure sample, is depicted in Fig. 6a. For doped ones, ν_cr fit in the (‒0.32547 ≤ ν_cr < –0.24502) domain. Polycrystalline [43], single-crystal [44], and thin film [45] are such a materials that this system was also traceable on them. In Gaussian section, the dense streaks signify theoretic equals with –0.5, –1, and –1.5 slopes, value for three, two, and one dimensionality schemes, respectively. For each sample, these discrete linear segments showing fluctuation conductivity behavior in the Gaussian area (–4.5 < ln(ε) < –1) are exhibited in Figs. 6a to 6e. Altogether, the investigational statistics are depicted in Fig. 6f for easy comparison and quick assessment.

For three-dimensional fluctuations while ν = ‒0.5, the intercepts of lined fitting adjust from ‒2.52269 to –2.8099 and then computed data for A_3D hints to achieve the coherence length alongside the c axis at the zero-Kelvin, ξ_c(0). These data adapts from 12.6333 to 9.47946 Å, related to the Y-358 + x wt % SnO₂ compounds, and recorded in Table 3.

Table 3. Distinctive factors associated with conductivity fluctuation study on behalf of Y-358 mixtures by altered quantities of SnO₂ nano-sized inclusion. FM (first method), SM (second method), CR (critical region), SW (short wave)

The lowest ξ_c(0) in the sequence is 9.47946 Å at x = 0.60. Between these quantities for none-added sample whilst x = 0, ξ_c(0) was ~15% superior than the one reported (10.95 Å) for Y-358 pure sample. Nevertheless, by rising nanoparticles SnO₂ addition, ξ_c(0) reduced which designates extra disarray stately of the specimens [19].

For two-dimensional fluctuations while ν = –1, the intercepts of linear fitting adjust from –4.24894 to –3.81605 and then computed value for A_2D hints to achieve the super layer length d. This value decreases from 106.54 to 69.1055 Å, related to the Y-358 + x wt % SnO₂ (x = 0 to 0.60) compounds which named First method (Formula), and its quantities are listed in Table 3. Junction temperatures between three- and two-dimension border T_2D–3D are estimated via crossing of the two linear segments and then by the substitution of T_2D–3D into Eq. (11), the interlayer coupling J is computed, and finally by the substitution of J and ξ_c(0) into Eq. (10), the super layer length d is found and known as Second method (-Measured). The value of d varies from 103.831 to 67.2684 Å, versus the Y‑358 + x wt % SnO₂ compounds. The quantities regarding both procedures are similar and for comparison, a plot of the super layer length d against SnO₂ addition is depicted for two methods with their average in Fig. 7.

Fig. 7.

Plots of d and J parameters against various addition for the Y-358 added with SnO₂ specimens via twofold approaches and their average.

Going over this graph implies that except for x = 0.20, by cumulative SnO₂ doping the super layer length d reduces but anisotropy γ upsurge, which is recorded in Table 3. As far as the charge carriers involve, the diminution in quantities related to d can be interpreted as reduction of relaxation time and distressing of their mean free path. The coupling among the CuO₂ planes is effected by the sum of replacement positions which triggers a growth in anisotropy γ with the addition of SnO₂ nanoparticles because the dimension of the Sn ions (0.83 Å), is greater than that of Cu ions (0.68 Å at low spin) [46]. According to AL and LD outline, the total interlayer coupling J changes from 0.05438 to 0.07735, which specifies no significant movement per atom by increasing SnO₂ addition (see Table 3 and Fig. 7). Diverse temperatures correlated to their dimensionality fluctuation associated with varied SnO₂ nanoparticles substance are tabulated in Table 4.

Table 4. SnO₂ nanoparticles substance dependency of various intersect temperatures such as GL, LD, and SW fluctuation accompanied with their temperature range

Consistent with this Table 4, poorer T_C numbers than T_LD signify that the thermodynamically triggered Cooper pairs are produced inside the granule at reasonably higher temperatures but because of the intragranular instabilities, the mean field critical temperature comes down to smaller values. It can be concluded that the three-dimensional Gaussian system controls the 3D boundary for acquiring of superconductivity long-range order in the bulk compound [47].

Close to T_C, once the reduction of temperature occurs, earliest superconductivity is founded in the CuO₂ planes, by way of a 2D establishment, and changeover to a distinct 3D system [48].

The scanning electron microscopy (SEM) images with two magnifying factor 2500 (a, b, c, d, and e) and 10 000 (f, g, h, i, and j) related to Y₃Ba₅Cu₈O_18 ± δ + x wt % (x = 0, 0.20, 0.40, 0.50, and 0.60) polycrystalline mixtures with nano-sized SnO₂ doping are shown in Fig. 8.

Fig. 8.

Scanning electron micrographs of Y₃Ba₅Cu₈O_(18 ± δ) specimens with 0 (a, f), 0.20 (b, g), 0.40 (c, h), 0.50 (d, i), and 0.60 wt % (e, j) (magnifying factor 2500 and 10 000 separately) SnO₂ nano-sized particles added. The random orientation of grains and almost modification of connectivity in several parts is apparent.

This figure illustrates that the random orientation of grains and nano-sized tin-oxide inclusions consequence an almost decrease of the grain size in YBCO samples which confirms by the average crystallite size values 50.32623, 44.65428, 46.63808, 51.63545, and 48.48951 nm associated with x = 0, 0.20, 0.40, 0.50, and 0.60, respectively (x = 0.50 is exceptional case). It can be observed that for both sets of images, by increasing the nanoparticles SnO₂, the homogeneity of the samples and also connectivity between the grains is improved. Lower dimensional effects in the transport properties can occur with the decrease in grain size when the number of grain boundaries increases and consequently imply a greater number of weak links (see [49, 50]).

Figure 9 shows scanning electron micrographs of Y₃Ba₅Cu₈O(_18 ± δ) sample with 0.50 wt % SnO₂ nanoparticles doping with magnification 10 000×.

Fig. 9.

Scanning electron micrographs of Y₃Ba₅Cu₈O (18 ± δ) samples with 0.50 wt % SnO₂ nanoparticles doping with magnification 10 000×. (a) Normal SEM image, (b) Modified SEM images, the pixels intensity below the minimum threshold value (background contribution) displayed in darker hue (color online: blue), and the pixels intensity above the maximum threshold value depicted in lighter hue (color online: green) for better exhibition of particles.

Among the SEM images, the one with x = 0.50 doped has chosen because of the highest value of average crystallite size. In this figure, (a) normal SEM image and (b) modified SEM image related to Fig. 8i are shown, respectively. To compare these two images for better exhibition of particles, the pixels intensity below the minimum threshold value are displayed in blue (background contribution), and the pixels intensity above the maximum threshold value are depicted in green colour. However, according to Figs. 9a and 9b, enrichment of granule volume and solidity arrangements while the SnO₂ addition rises is demonstrated at this particular amount (x = 0.50). The granules similarly appear to lengthen further at one lateral, creating an almost four-sided pattern with an ordinary size of 1.5 μm.

From Eqs. (14) to (17), some superconducting parameters such as the critical current density J_c(0) and critical magnetic fields, B_c(0), B_c1(0), B_c2(0) versus none-added and added specimens are computed and placed in Table 5.

Table 5. Some computed superconducting data related to added and pure Y-358 specimens with different quantities of nano-sized SnO₂ insertions

Comparing all the quantities of B_c(0), B_c1(0), B_c2(0), and J_c(0) for pure and doped Y-358 specimens confirms that by growing the number of nanoparticles of tin-oxide dopant, the mentioned parameters are improved. This situation designates the enhancement of flux pinning effects.

5 CONCLUSIONS

High-temperature polycrystalline Y-358 superconductors have been synthesized via the conventional solid-state reaction route with tin-oxide nanoparticles insertion from x = 0 to 0.60 wt % (Y-358 + x wt % SnO₂). Phase formation and microstructures have been methodically surveyed by XRD and SEM. The X-ray diffraction technique showed the slight variation of the crystal lattice parameters and overall reduction of the orthorhombicity by increasing the content of SnO₂ in YBCO matrix. SEM observations and the crystallite size calculation showed that the grain size and the average crystallite size decreased with rising the amount of SnO₂ in Y-358 specimens as compared to the SnO₂-free sample. The resistivity-temperature graphs obtained by the standard four-point probe method exhibited metallic and superconducting behavior during the normal and superconducting state, respectively, with and without SnO₂ doping. The effect of tin-oxide nanoparticles on the conductivity fluctuation of high-temperature superconductor polycrystalline Y-358 was considered by the AL and LD outlines. Adding SnO₂ to the Y-358 compound causes enhancing some superconducting properties, specifically, T_C in all composites.

SnO₂ addition causes not only structural but also dimensional modifications associated with the mesoscopic and microscopic level of irregularities in the composite. These effects can be interpreted as disarray because of substituting a number of Cu sites into Y-358 which effects some variation in electronic arrangement of the granules, and by way of an outcome, the non-existence of an optimized carrier concentration in the CuO₂ flat surfaces. By cumulative SnO₂ inclusions, T_C and anisotropy γ increase but super-layer length d decrease whereas in general interlayer coupling J does not change significantly. These outcomes might be described as the redistribution of charges in the superconducting matrix due to the oxygen content, the number of substitution sites, resistance of the feeble link affected by irregularities, and non-existence of displacement per atom, respectively. Our data showed the conductivity fluctuations, and while the doping level of tin-oxide nanoparticles in Y-358 compounds increased, the critical parameters such as B_c1(0), B_c2(0), and J_c(0) improved and indicated enhanced flux pinning.