Introduction

High-temperature superconductors (HTS) have exhibited utility in a wide range of applications due to their high-power densities and efficiency. They have previously been used for prototypes of power cables, transformers, motors, and fault current limiters in sectors such as power electronics. They have found extensive use in scientific magnets and filters, as well as in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) procedures [1]. Cu0.5Tl0.5Ba2Ca2Cu3O10-δ, CuTl-1223, is a HTS with a moderating charge reservoir layer containing both Cu and Tl which stabilizes its synthesis procedure and enhances its critical parameters (i.e., critical temperature “Tc,” critical current density “Jc,” and critical magnetic field “Hc”) [1]. This makes CuTl-1223 a promising superconductor from application view point [1,2,3,4]. Usually, imperfections, which appear during preparation procedure, such as Oxygen vacancies, voids, and impurity phases influence the superconducting critical parameters. However, this problem can be resolved using certain nanoparticles additives in the bulk superconductor in order to increase the intergrain connectivity and increase the phase formation.

Different research groups [5,6,7,8,9] have examined the effect of adding different nanoparticle inclusions on the physical and structural characteristics of many HTS. It has been observed from the literature reviews [10,11,12,13,14,15,16,17,18,19] that nanoparticle inclusions improve the connectivity between the grains and enhance the superconductivity critical parameters to some degree without impact the crystal structures of the HTS. It was concluded that the addition of nano-SnO2 and nano-In2O3 in CuTl-1223 superconducting matrix improve to some extent the phase formation, microstructure, electrical properties, and mechanical properties of the phase [20]. Minor amounts of nano-Fe2O3 addition in CuTl-1223 enhance the volume fraction of the phase and in turn Tc [21]. The effect of BaSnO3 nanoparticles addition on the physical properties of CuTl-1223 phase was studied [22] and it was found that low contents from BaSnO3 nanoparticles enhance the superconductor properties such as relative volume fraction, Tc and Jc of CuTl-1223 phase. Hussain et al. [23] studied the activation energy and excess conductivity of (Ag)x/CuTl-1223 nano/superconductor composites. They concluded that CuTl-1223 remains in its crystal structure even after the addition of Ag nanoparticles. The activation energy and zero resistivity critical temperature were enhanced with increasing Ag content up to x = 2.0 wt%. It was found that the microscopic parameters estimated from the fluctuation-induced conductivity (FIC) analysis are in agreement with the experimental results. The increase in coherence length along c-axis and interlayer coupling indicates the suppression of anisotropic nature of CuTl-1223 phase after Ag addition. Qasim et al. [24] investigated the effect of Cr nanoparticles addition on structure and superconducting transport properties of CuTl-1223 phase. As a function of the Cr content in (Cr)x/CuTl-1223 nano-superconductor composites, superconductive microscopic parameters were determined by excess conductivity analysis at 3D, 2D, and 0D fluctuating regions. Barakat et al. [25] worked on (Co0.5Zn0.5Fe2O4)x/CuTl-1223 nano/superconductor samples. They found that the pseudogap temperature and superconducting fluctuation temperature varied with increasing Co0.5Zn0.5Fe2O4 nanoparticles and from excess conductivity analysis there were four different fluctuation regions.

Bismuth vanadate (BiVO4), a traditional ternary layered-structure semiconductor oxide, has received great attention [26]. Due to its unique characteristics, such as ferroelasticity, ionic conductivity, photocatalysis, and color, BiVO4 is widely used in many potential applications such as in pigment industry, photocatalytic mineralization of organic pollutants, and in electronic devices [27]. BiVO4 is a perfect photocatalytical material (band gap 2.5 eV) for mineralization of organic pollutants under visual light irradiation, contrary to the widely used wide band gap semiconductors like TiO2 and ZnO (band gap 3.2 eV). The BiVO4 is also distinguished by the unique crystal structure that provides photocatalysis, apart from its strong stability against photocorrosion, low cost, and non-toxicity [26]. BiVO4 exists in three crystal systems; scheelite structure with monoclinic and tetragonal systems, and zircon structure with a tetragonal system. There have been reports of many BiVO4 synthesis techniques like the solid state, aqueous process, hydrolysis, and hydrothermal. Synthesis conditions will influence the crystal structure and the form of the BiVO4 [28].

In this study, the effect of adding BiVO4 nanoparticles on the microstructure, morphology, electrical resistivity, excess conductivity, and mechanical strength of Cu0.5Tl0.5Ba2Ca2Cu3O10−δ superconducting phase has been investigated. Nanoparticle/superconductor composites of type (BiVO4)x/Cu0.5Tl0.5Ba2Ca2Cu3O10−δ (with x = 0.00, 0.02, 0.05 and 0.10 wt%) were synthesized by the standard solid-state reaction technique. To understand the role of BiVO4 nanoparticles addition in CuTl-1223 matrix, the electrical resistivity data were analyzed with the aid of Aslamazov–Larkin (AL) and Lawrence–Doniach (LD) models. The fluctuation-induced conductivity for the prepared composites was studied. Numerous critical superconducting parameters, such as Ginzburg number (NG), coherence length along c-axis ξc(0), interlayer coupling (J), Bc(0), Bc1(0), Bc2(0), and Jc(0), were estimated as function of BiVO4 content. Finally, the mechanical strength of the prepared composites was studied through Vickers microindentation (HV) test. Mechanical parameters such as elastic modulus (E), yield strength (Y), fracture toughness (K), and brittleness index (B) were estimated as a function of BiVO4 content.

Results and discussion

XRD, TEM, HRTEM, FTIR, and PL for BiVO4 nanoparticles

Figure 1(a) displays room temperature XRD pattern for BiVO4 nanoparticles. The peaks of diffraction were all indexed to the monoclinic BiVO4 (m-BiVO4) with lattice constants of a = 5.195 Å, b = 11.701 Å, and c = 5.092 Å, JCPDS card number 14-0688 [29], indicating the successful synthesis of m-BiVO4 crystals in single phase. Using MAUD software [29], Rietveld refinement of XRD data were carried out for quality analysis, as shown in the inset of Fig. 1(a). The refinement is successful, and the high quality of the sample is verified from the values of the quality factor (χ2), the weighted profile R-value (Rwp), and the profile fitting R-value (Rp), as indicated in the figure. The average crystallite size of BiVO4 nanoparticles was calculated using Debye–Scherrer equation [27]:

Figure 1
figure 1

BiVO4 nanoparticles (a) XRD pattern (inset shows Rietveld refinement), (b) TEM micrograph (inset shows particle size distribution histogram), (c) HRTEM, (d) diffraction Frings, (e) SAED, (f) FTIR, and (g) PL.

Full size image
$$\mathrm{D}=\frac{0.9\uplambda }{\mathrm{\beta cos}(\uptheta )},$$
(1)

where β is the full width at half maximum (FWHM) obtained from the Gaussian fitting for the most three intensive diffraction peaks. The average crystallite size according to Debye–Scherrer equation was found to be 29 nm. Figure 1(b) depicts TEM micrograph for BiVO4 at scale of 200 nm, the inset shows the grain size distribution histogram done using ImageJ and origin software. The micrograph reveals flake-like grains with average grain size of about 20 nm. As a result, there is an agreement between the average size computed from XRD and TEM analyses. The crystallites of the synthesized BiVO4 are shown in Fig. 1(c) by a high-resolution transmission electron microscope (HRTEM) image. The diffraction fringes pattern in Fig. 1(d) was used to compute the interlayer distance (d-spacing), which yielded 0.29 nm. This value is a good match for the (040) lattice plane of BiVO4's d-spacing value, according to JCPDS card number 14-0688 [29]. The polycrystalline nature of monoclinic BiVO4 is also identified by the selected area electron diffraction (SAED) patterns in Fig. 1(e), which are the bright spots of electron diffraction. These findings agree well with the XRD investigations.

FTIR spectrum is shown in Fig. 1(f) for BiVO4 nanoparticles. It indicates obvious V–O stretching in 400–900 cm−1 wavenumber range [30]. In addition, the presence of stretching symmetrical vibrations for Bi–O bond, as demonstrated in the previous reports [31], was indicated at 732.97 cm−1. The V–O stretch of V2O5, or less valent vanadium oxide, is responsible for the band appeared at 1.023.27 cm−1 [32]. PL spectrum of BiVO4 nanoparticles is shown in Fig. 1(g) PL spectrum was recorded with excitation wavelength of 325 nm. A PL peak at around 643.04 nm is recorded.

XRD for (BiVO4)x/CuTl-1223 composites

Figure 2 displays the XRD patterns of (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt%. The diffraction peaks are mostly indexed to the tetragonal structure of CuTl-1223 phase with P4/mmm space group [33]. Limited non-indexed low intensity peaks suggest the existence of CuTl-1212 phase (at 2θ = 19°, 26°, and 37°) and BaCuO2 (at 2θ = 26° and 29°). The relative volume fraction percentages for CuTl-1223, CuTl-1212, and BaCuO2 phases are computed in the same way as in our earlier work [21], and their results are shown in Table 1. When BiVO4 is increased from 0.00 to 0.10 wt%, the volume fraction percentage of CuTl-1223 reduces from 93.5 to 84.2%. Thus, BiVO4 causes a decrease in the main CuTl-1223 phase percentage, while increasing the CuTl-1212 and BaCuO2 phase percentages. Table 1 also shows the computed lattice parameters for (BiVO4)x/CuTl-1223 composites. It is clear, from Table 1, that BiVO4 nanoparticles have not changed dramatically the structural symmetry of the CuTl-1223 phase for x ≤ 0.05 wt%. Nevertheless, the c-parameter length reduces gently and may be caused by variation in oxygen content [34]. The micro-strain along the c-axis (εz) was estimated from the following equation: \({\upvarepsilon }_{\mathrm{z}}=\frac{{\mathrm{c}}_{\mathrm{m}}-{\mathrm{c}}_{\mathrm{s}}}{{\mathrm{c}}_{\mathrm{s}}}\) [35], where cm and cs are the measured and standard lattice parameters, respectively. The standard lattice parameter for CuTl-1223 superconductor is equal to 15.89 Å [33]. Surprisingly, all samples showed compressive micro-strain. The degree of compression decreases with the addition of BiVO4, which could be related to the formation of oxygen vacancies in the CuTl-1223 lattice [35].

Figure 2
figure 2

XRD patterns of (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt%.

Full size image
TABLE 1 Variation of relative volume fraction percentages, lattice parameters (a & c), micro-strain εz, superconducting transition temperature (Tc), superconducting zero transition temperature (T0), normal state resistivity (ρroom), residual resistivity (ρ0), and temperature resistivity coefficient (β) with x.
Full size table

SEM for (BiVO4)x/CuTl-1223 composites

Figure 3(a–d) shows the SEM micrographs of (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt%, respectively, at 5 μm scale. The micrographs reveal the standard plate-like grains of CuTl-1223 superconductor. Only a few nanoparticles are noticeable in the SEM pictures because of their extremely low percentages. After inserting BiVO4 nanoparticles into CuTl-1223 matrix, we can clearly identify and observe noticeable reduction in the number of voids and improvements in intergrain connections. ImageJ software was used to determine the average grain thickness (T), which is shown in each micrograph as 0.549, 0.535, 0.379, and 0.375 μm for x = 0.00, 0.02, 0.05, and 0.10 wt%, respectively. The average grain thicknesses of the investigated composites are reduced when compared to the pure sample. Constituent composite arrangements, which include a specific volume fraction of spatially distributed phases with various compositions, grain size and morphology with random orientation, and their spatial distribution, are directly responsible for solid-state diffusional phase transformation, which includes nucleation, growth, and impingement [36].

Figure 3
figure 3

SEM micrographs of (BiVO4)x/CuTl-1223 composites with (a) x = 0.00 wt%, (b) 0.02 wt%, (c) 0.05 wt%, and (d) 0.10 wt%.

Full size image

EDX for (BiVO4)x/CuTl-1223 composites

Figure 4(a–d) shows EDX spectra for (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt%, respectively. It is clear that there are no peaks corresponding to Bi- or V-based compounds detected in the XRD patterns. However, the EDX analysis for (BiVO4)x/CuTl-1223 composites show the existence of Bi, V, and O elements in the bulk samples. This means that they did not enter the structure of the CuTl-1223 phase, but just occupied interstitial places between the grains. This result is confirmed with the nearly constant lattice parameters values. The mass and atomic percentages of Tl, Ba, Ca, Cu, Bi, V, and O determined from EDX analysis are tabulated as insets in Fig. 4(a–d).

Figure 4
figure 4

EDX spectra for (BiVO4)x/CuTl-1223 composites with (a) x = 0.00 wt%, (b) x = 0.02 wt%, (c) x = 0.05 wt%, and (d) x = 0.10 wt%.

Full size image

FTIR for (BiVO4)x/CuTl-1223 composites

The FTIR technique is used to investigate weak and strong bonding vibrations between molecules in a sample, such as O–H, C–O, C–H, and H–O–H. The molecular bonding process is represented by the vibrational frequencies in the sample. FTIR spectroscopy can also reveal several oxygen vibrational phonon modes that are important in superconductivity. The FTIR spectra of (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt% are shown in Fig. 5. The stretching vibration of the intermolecular hydrogen bond (O–H) is shown by a peak at 3689.85 cm−1 and a specific peak at 3448.84 cm−1, indicating that the OH groups are essentially stretched [37, 38]. The appearance of a peak band at 1643.41 cm−1 validates the CuTl-1223 phase intricate formation, as previously described [39]. The presence of two successive peaks at 1055.26 cm−1 and 1435.09 cm−1 confirms that additional metal oxides and carbonates, such as CaCo3 and CuO, have stretched their bonds [39]. Oδ atoms in the charge reservoir layer create the bands in the 600 to 800 cm−1 range [40]. Around 585.42 cm−1, the planner oxygen modes Cu(2)–Op–Cu(2) are identified, respectively. The FTIR and XRD results show that the structure of the host CuTl-1223 superconductor did not change after the addition of BiVO4 nanoparticles. These studies show that BiVO4 nanoparticles do not break down or replace any lattice sites in CuTl-1223 unit cell, but rather exist in intergranular regions, such as grain boundaries.

Figure 5
figure 5

FTIR spectra of (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt%.

Full size image

Electrical resistivity for (BiVO4)x/CuTl-1223 composites

The electrical resistivity (ρ) versus temperature (T) curves for (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt% are shown in Fig. 6(a). From room temperature through the superconducting transition temperature (Tc), the curves show a linear relationship with temperature. The resistivity curves under Tc decrease with temperature until T0 is reached, which is the superconducting zero transition temperature. Tc is typically determined as the highest point in the dρ(T)/dT against T curve [20], see inset of Fig. 6(a). Table 1 lists the values for Tc and T0 for the prepared samples. When x fluctuates between 0.00 and 0.10 wt%, Tc drops from 119.5 to 103.5 K. T0 also follows the same trend as Tc, falling from 111 to 91.5 K when x rises from 0.00 to 0.10 wt%. The suppression of Tc and T0 is mostly owing to the decrease in the relative volume fraction percentage of CuTl-1223 phase and to the increase of impurity phase’s percentages, as confirmed from XRD results. Also, retardation in Tc and T0 can be associated with the decrease of carriers’ density in the CuO2 planes supplied by the charge reservoir layer, which depends upon the oxygen contents in the charge reservoir layer [21].

Figure 6
figure 6

(a) Resistivity versus temperature curves of (BiVO4)x/CuTl-1223 with x = 0.00, 0.02, 0.05, and 0.10 wt%, inset shows dρ/dT curves, (b) Arrhenius plots, (c) Variation of activation energy (U) and T0 with x.

Full size image

In Table 1, an increase in normal state resistivity (ρroom) is seen and reported. This implies that the dispersion of carriers increases as the amount of BiVO4 nanoparticles increases. The assisted thermal process of HTS is known as vortex motion, and the energy required to raise the flow pinning clog is known as activation energy (U), which may be quantified using the Arrhenius rule. Arrhenius law is \(\rho ={\uprho }_{0}{\mathrm{e}}^{\frac{\mathrm{U}}{{\mathrm{k}}_{\mathrm{B}}}}\mathrm{T}\), where U is the activation energy and kB is Boltzmann constant. Arrhenius plots for (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt% are shown in Fig. 6(b). For the computation of activation energy, only the transition regime around T0 is taken into account. Figure 6(c) shows the fluctuation of U and T0 against x. With increased nanoparticle addition (x), the activation energy U and T0 in the CuTl-1223 matrix falls somewhat. The decrease might be due to the increase of impurities and oxygen vacancies. Nadeem et al. [34] obtained similar findings for (NiFe2O4)x/CuTl-1223 composites.

Excess conductivity for (BiVO4)x/CuTl-1223 composites

The behavior of fluctuation-induced conductivity (FIC) can have a big influence on superconducting properties [41]. The fluctuation at high temperatures (above Tc) is caused by the electrical resistivity diverging from the linear metallic normal state behavior. The excess conductivity region is assumed to be initiated by superconducting fluctuation, which is created as a result of Cooper pair creation [42]. The Aslamazov–Larkin (AL) [42, 43], Lawrence–Doniach (LD), and Maki–Thomson [44,45,46] models may all be used to study superconducting fluctuations. By subtracting the measured conductivity, σm(T), from the normal state conductivity, σn(T), excess conductivity, Δσ, may be estimated as follows:

$$\Delta\upsigma ={\upsigma }_{\mathrm{m}}(\mathrm{T})-{\upsigma }_{\mathrm{n}}(\mathrm{T})=\frac{{\uprho }_{\mathrm{n}}\left(\mathrm{T}\right)-{\uprho }_{\mathrm{m}}(\mathrm{T})}{{\uprho }_{\mathrm{m}}(\mathrm{T}){\uprho }_{\mathrm{n}}(\mathrm{T})}$$
(2)

In the temperature range of 170 K to 300 K, the normal state resistivity ρn(T) is computed using the following relation [47]:

$${\uprho }_{\mathrm{n}}\left(\mathrm{T}\right)={\uprho }_{0}+\mathrm{\beta T},$$
(3)

where ρ0 and β are the residual resistivity due to impurity scattering and the temperature resistivity coefficient, respectively. Table 1 lists the values of ρ0 and β with x. The residual resistivity ρ0 increased with x, owing to increased impurity scattering in the CuO2 plane and carrier localization across these nanoparticles addition.

The AL model [42] may be used to indicate excess conductivity as follows:

$$\frac{\Delta\upsigma }{ {\upsigma }_{\mathrm{room}}}={\mathrm{At}}^{\mathrm{\alpha }} ,$$
(4)

where σroom is the conductivity at 300 K and t is the reduced temperature \(\mathbf{t}=\frac{\mathbf{T}-{\mathbf{T}}_{\mathbf{c}}}{{\mathbf{T}}_{\mathbf{c}}}\).

The following relationships link the conductivity exponent α in Eq. (4) to the conduction dimensionality D [42]:

$$\mathrm{\alpha }=\left\{\begin{array}{c}-0.3, cr\, fluctuation\\ -0.5, 3D\, fluctuation\\ -1.0, 2D\, fluctuation\\ -1.5, 1D\, fluctuation\\ -3.0, SW\, fluctuation\end{array}\right.$$
(5)

The dynamic critical, three-dimensional, two-dimensional, one-dimensional, and short-wave fluctuations are indicated by cr, 3D, 2D, 1D, and SW, respectively. In Eq. (4), the temperature-independent amplitude A is given by [48]

$$\mathrm{A}=\left\{\begin{array}{c}\frac{{\mathrm{e}}^{2}}{32\mathrm{ \hslash }{\upxi }_{\mathrm{c}}\left(0\right)}, 3D region\\ \frac{{\mathrm{e}}^{2}}{16\mathrm{ \hslash d}}, 2D region\\ \frac{{\mathrm{e}}^{2}{\upxi }_{\mathrm{c}}\left(0\right)}{32\mathrm{ \hslash s}}, 1D region\end{array},\right.$$
(6)

where ξc(0) is the coherence length along the c-axis at T = 0 K, and d is the effective layer thickness of 2D systems, which is normally equal to the unit cell's c-axis length. The LD model adds the concept of J, which is based on Josephson coupling as a consequence of \({\xi }_{\mathrm{c}}\left(0\right)\) contact with superconducting layers. The relation between \({\xi }_{\mathrm{c}}\left(0\right)\) and interlayer coupling, J is given by [49]

$$\mathrm{J}={\left[\frac{{2\upxi }_{\mathrm{c}}\left(0\right)}{\mathrm{d}}\right]}^{2}.$$
(7)

The anisotropy, γ of layered superconducting systems is estimated from the following equation [50]:

$$\upgamma = \frac{{\upxi }_{\mathrm{ab}}\left(0\right)}{{\upxi }_{\mathrm{c}}\left(0\right)} ,$$
(8)

where \({\xi }_{\mathrm{ab}}\left(0\right)\) is the ab coherence length which is generally between 10 and 20 Å for a HTS [51].

Figure 7(a–d) shows plots of ln Δσ/σroom versus ln t of (BiVO4)x/CuTl-1223 with x = 0.00,0.02, 0.05, and 0.10 wt%. Different fluctuation zones are depicted in the graphs. At each region, the conductivity exponent (α) values were calculated by fitting the data to Eq. (4). For cr, 3D, 2D, and SW fluctuations, four basic fluctuating zones can be seen. The conductivity exponent values (αcr, α3D, α2D, and αSW) as well as the crossover temperatures (Tcr-3D, T3D-2D, and T2D-SW) for the detected regions are listed in Table 2. The termination of the Ginzburg–Landau (GL) and the dominance of SW fluctuations are shown by the region that occurs at high temperatures (T >  > Tc). The SW effect occurs when the coherence length order and the order parameter's characteristic wavelength are in the same order [52]. In this temperature range, ln Δσ/σroom quickly drops, with an exponent αSW ranging from 2.98 to 3.56, which is quite close to theoretical expectations. Changes in carrier density have a substantial influence on changes in the order parameter, blamed for the observed trend [53]. At T2D- SW, a transition from SW fluctuations to the mean-field regime (MFR) happens when the temperature is decreased. The MFR for various manufactured composites is made up of two linear components. At temperatures ranging from T2D-SW to T3D- 2D, the conductivity exponent α2D values vary from 1.11 to 1.12 in the first section, suggesting the presence of 2D fluctuations. The mobility of the carriers in the conducting CuO2 planes indicates the conductivity in the 2D fluctuating area, due to the layered structure of HTS materials. The 3D fluctuation region occurs when the temperature is decreased, with the conductivity exponent α3D fluctuating from 0.52 to 0.63. The high anisotropy of HTS, in which charge carriers travel more freely in some directions than in others, might explain the 3D–2D crossover. In this range of temperature variations, charge carriers also show some potential to travel along molecular planes. At lower temperatures, charge carriers can migrate between molecular planes and crossover from one to the other, causing a crossover. This crossover occurs in three dimensions, and the charge carriers are then more susceptible to temperature changes. This implies that before forming pairs, charge carriers tend to travel more freely across the crystal [54]. The last region is at Ginzburg temperature TG, which signals a transition from 3D to critical fluctuation (cr). According to the predictions of the 3D-xy universality dynamics class, the conductivity exponent αcr ranges from 0.29 to 0.36.

Figure 7
figure 7

Variation of \(\mathrm{ln }\frac{\Delta\upsigma }{ {\upsigma }_{\mathrm{room}}}\) versus ln t for (BiVO4)x/CuTl-1223 composites with (a) x = 0.00 wt%, (b) x = 0.02 wt%, (c) x = 0.05 wt%, and (d) x = 0.10 wt%.

Full size image
TABLE 2 Conductivity exponents, crossover temperatures, and superconducting parameters for (BiVO4)x/CuTl-1223 composites with x = 0.00, 0.02, 0.05, and 0.10 wt.%.
Full size table

The Ginzburg number (NG) and the thermodynamic critical field Bc(0) are correlated by the following expression [25]:

$${\mathrm{N}}_{\mathrm{G}}=\left|\frac{{\mathrm{T}}_{\mathrm{g}}}{{\mathrm{T}}_{\mathrm{c}}}-1\right|=\frac{1}{2}\left[\frac{{\mathrm{k}}_{\mathrm{B}}}{{\mathrm{B}}_{\mathrm{c}}^{2}(0){\upgamma }^{2}{\upxi }_{\mathrm{c}}^{3}(0)}\right],$$
(9)

where kB is the Boltzmann constant, and γ is the anisotropy parameter. By determining Bc(0), the values of lower critical magnetic field Bc1(0), upper critical magnetic fieldBc2(0), and critical current density Jc(0) could be deduced by means of the following expressions [25]:

$${\mathrm{B}}_{\mathrm{c}}\left(0\right)=\frac{{\mathrm{\varphi }}_{0}}{\uppi \sqrt{8}{\upxi }_{\mathrm{c}}(0)\uplambda (0)},$$
(10)
$${\mathrm{B}}_{\mathrm{c}1}\left(0\right)=\frac{\mathrm{ln\kappa }}{\sqrt{2}\upkappa }{\mathrm{B}}_{\mathrm{c}}\left(0\right),$$
(11)
$${\mathrm{B}}_{\mathrm{c}2}\left(0\right)=\sqrt{2}{\mathrm{ \kappa B}}_{\mathrm{c}}\left(0\right),$$
(12)
$${\mathrm{J}}_{\mathrm{c}}\left(0\right)=\frac{4\upkappa }{3\sqrt{3 }\uplambda \left(0\right)\mathrm{ln\kappa }}{\mathrm{B}}_{\mathrm{c}1}\left(0\right),$$
(13)

where λ(0) is the penetration depth, κ = λ /ξ is the GL parameter, and φo = ℎ/2e is the flux quantum number.

Table 2 summarizes all of the determined superconducting parameters, including NG, ξc(0), J, Bc(0), Bc1(0), Bc2(0), and Jc(0). For all of the prepared composites, the NG values rise when compared to the pure sample. As the BiVO4 content x rose from 0.00 wt% to 0.10 wt%, the coherence length ξc(0) increased from 19.69 to 39.30 Å. The calculated ξc(0) values are higher than those found in the films [55] and single crystals [56]. The polycrystalline nature of the current composites may assist in understanding this. Because polycrystalline composites are made up of crystallites, their transport properties are regulated by the type of defects and inhomogeneities, the mixing of conducting planes (ab) with insulating c-axis, and the crystalline boundaries [54]. The values of the interlayer coupling J are less than 1 which indicates the weak coupling among CuO2 planes. Similar result was reported by Ranjbar et al. [57]. The critical superconducting parameters Bc(0), Bc1(0), Bc2(0), and Jc(0) decrease with x when compared to the pure sample. With increased BiVO4 NPs, the superconducting parameters drop due to an increase in grain boundary resistance and a reduction in flux pinning inside the samples. Similar results were reported by Qasim et al. [24] for Cr-added CuTl-1223 samples. In comparison to Y-123/WO3 composites conducted by Almessiere et al. [58], the critical superconducting parameters were improved with WO3 NPs addition of x = 0.05 and reduced for x > 0.05 wt%. They attributed these finding to an increase in pinning ability inside the composite, as well as the presence of pinning sources caused by the proper tiny quantity of WO3 nanoparticles inclusion.

Vickers Microindentation for (BiVO4)x/CuTl-1223 composites

Figure 8(a) illustrates graphically the changes in load dependent Vickers microindentation (HV), computed as \({\mathrm{H}}_{\mathrm{V}}=\frac{2\mathrm{Fsin}(\mathrm{\alpha }/2)}{{\mathrm{d}}^{2}}=1854.4\frac{\mathrm{F}}{{\mathrm{d}}^{2}} \left(\mathrm{GPa}\right),\) where α is the indenter’s face angle of 136° and d is the adequate mean indentation diagonal length, for (BiVO4)x/CuTl-1223 with x = 0.0,0.02, 0.05, and 0.1 wt%. According to the experimental data, it is simple to deduce that raising the BiVO4 content in the CuTl-1223 phase generates a large impact on Hv values. Clearly, adding up to x = 0.10 wt% increases the Hv values and the structure of the CuTl-1223 phase greatly. This boost can be ascribed to a reduction in porosity or resistance to fracture propagation within the grains, as well as an increase in grain connection by incorporating nanoparticles up to 0.10 wt% into the CuTl-1223 phase. These results are consistent with the results observed from SEM micrographs. Figure 8(a) further shows that the Hv values constantly decline up to an applied stress of 2.94 N, whereas Hv values practically remain constant above this applied load value. The saturation limit area might so be deemed to be 2.94 N. This suggests that the samples display the characteristic ISE nature, simultaneous elastic and plastic deformations in the material owing to system recovery, as stated by the indenter penetration depth [59]. The ISE behavior has been examined through Meyer analysis according to the following relation F = Adn [59]. A plot between Ln F versus Ln d, inset of Fig. 8(a), yields straight line whose slope (n) can determine the type of indentation whether it is normal or reverse ISE. According to our fitting data, tabulated as inset in Fig. 8(a), it is clear that all the slope values are less than 2 which confirm that the prepared samples exhibited normal ISE.

Figure 8
figure 8

Variation of (a) HV against F, inset for Meyer analysis coupled with linear fitting data (b) elastic modulus E with x, (c) yield strength Y with x, (d) fracture toughness K with x, and (e) brittleness index B with x.

Full size image

The critical mechanical characteristics regarding the elastic modulus (E), yield strength (Y), fracture toughness (K), and brittleness index (B) were deduced, which are essential for the use of the CuTl-1223 superconducting phase in industrial applications. The true microhardness values were used to determine the load-independent parameters E, Y, K, and B from the following equations [21, 59]:

$$\mathrm{E}=81.9635 {\mathrm{H}}_{\mathrm{v}}$$
(14)
$$\mathrm{Y}={\mathrm{H}}_{\mathrm{v}}/3$$
(15)
$$\mathrm{K}=\sqrt{2\mathrm{E\alpha }}, (\mathrm{\alpha },\mathrm{ surface energy})$$
(16)
$$\mathrm{B}=\frac{{\mathrm{H}}_{\mathrm{v}}}{\mathrm{K}}.$$
(17)

The variations of E, Y, K, and B with x are represented in Fig. 8(b–e), respectively. The curves show that their values rise consistently as x increases up to 0.10 wt%. The increase in their values can be explained based on the occupation of nanoparticle intergrains and voids of the CuTl-1223 phase [60]. Moreover, BiVO4 addition displays better ductility and an enhanced capacity to resist indentation fractures. The E, Y, K, and B values for the prepared composites were compared to those reported by Cetinkara et al. [61] for the Bi-2223 superconductor. It was revealed that our mechanical parameters values are greater than theirs. This manifested the excellent texture and density of our prepared samples.

Conclusions

To demonstrate reliability, a series of (BiVO4)x/CuTl-1223 with x = 0.00,0.02, 0.05, and 0.10 wt% were effectively synthesized by solid-state reaction method. The findings of XRD and FTIR confirm that there are no dramatic changes that occur in the structure of the host CuTl-1223 superconductor following the addition of BiVO4 nanoparticles. These investigations demonstrate that BiVO4 NPs do not breakdown or substitute any lattice site in the unit cell of CuTl-1223, but instead reside at intergranular locations. The critical temperature Tc was reduced with BiVO4 content. This suppression is mostly due to the decrease in the relative volume fraction percentage of CuTl-1223 phase and to the increase of impurity phase’s percentages as confirmed from the XRD results. Also, the retardation in Tc can be associated with the decrease of carriers’ density in the CuO2 planes supplied by the charge reservoir layer, which depends on the oxygen contents in the charge reservoir layer. The ρ–T data matched quite well with the 2D and 3D Aslamazov–Larkin equations. The superconducting parameters determined by FIC analysis of are found to be consistent with the experimental results. The variation of oxygen content from the charge reservoir layer explained the increase in ξc(0) with x. The critical superconducting parameters Bc(0), Bc1(0), Bc2(0), and Jc(0) decreased with x when compared to the pure sample due to an increase in grain boundary resistance and a reduction in flux pinning inside the samples. From Vickers microindentation data, it was deduced that raising the BiVO4 up to x = 0.10 wt% increases the Hv values and the structure of the CuTl-1223 phase greatly. This boost can be ascribed to a reduction in porosity or resistance to fracture propagation within the grains, as well as an increase in grain connection by incorporating nanoparticles up to 0.10 wt% into the CuTl-1223 phase. These results were consistent with the results observed from SEM micrographs. Moreover, BiVO4 addition displayed better ductility and an enhanced capacity to resist indentation fractures.

Materials and methods

Synthesis procedure

BiVO4 nanoparticles were prepared by mechanochemical synthesis route. Mechanochemical synthesis is a solvent-free route that has developed as the most cost-effective and environmentally friendly alternative to existing methods for producing nanomaterials with exceptional characteristics for innovative applications. 5 g of Bi2O3 (Loba chemie, purity 99%) was combined and processed in a mortar and pestle for half an hour with 1.9586 g of V2O5 (Sigma, purity 99.9%). The powder was sifted twice to ensure its homogeneity. Then, the stoichiometric blend was heated to 820 °C for 7 h to achieve BiVO4 nanopowder. The BiVO4 powder was then mechanically ball milled for 5 h to minimize the size of the particles. In the milling method, the ball-and-powder weight ratio was 5:1. Retsch-planetary ball mill PM 400, with agate pots and balls, conducted the milling operation.

For Cu0.5Tl0.5Ba2Ca2Cu3O10-δ superconducting samples preparation, a solid-state reaction method was applied. In their nominal compositions, high-grade starting materials of Tl2O3 (Tl2O3, Aldrich, 99.99% purity), BaO2 (BaO2, Sigma-Aldrich 99% purity), CaO (CaCo3, Aldrich, 99% purity), and CuO (CuO, Alfa Aesar, 99% purity) have been mixed, ground, and then sifted in a 65 mm sieve. BiVO4 nanoparticles (grain size of ~ 20 nm) with wt% (x) ranging from 0.00 to 0.10 wt% were inserted to the sifted powder to obtain (BiVO4)x/CuTl-1223 nanoparticle/superconductor composites and again were mixed and crushed to ensure homogeneity. The powder was pressured into a disk and then placed in a silver sheet in order to reduce Tl losses throughout the heat treatment. In a sealed quartz tube, the samples were sintered at a rate of 2 °C/min till 760 °C, then at 1 °C/min to 850 °C and finally kept for 6 h at that temperature. After that the samples were gradually cooled to room temperature by a rate of 1 °C/min.

Characterization and measurements

The crystal structure of BiVO4 nanoparticles was identified using X-ray powder (XRD) technique with Shimadzu-7000 CuKα radiation (λ = 1.5418 Ǻ) in the range of 10° ≤ 2θ ≤ 80°. The morphology and crystallinity were achieved using HRTEM model JEOL (JEM-2100 LaB6) Japan. Optical characterizations for BiVO4 nanoparticles were done through Fourier transform infrared (FTIR) spectrophotometer model SHIMADZU-8400S and room temperature photoluminescence (PL) emission spectrum by Agilent technologies fluorescence spectrophotometer model Cary Eclipse.

Structural characterization for (BiVO4)x/CuTl-1223 composites was done through XRD measurements using Shimadzu-7000 XRD with CuKα radiation (λ = 1.5418 Ǻ) in the range 10° ≤ 2θ ≤ 80°. The morphology and elemental content were determined using JEOL scanning electron microscope type JSM-IT200. The device ran at a high voltage of 20 kV, with a rotary pump used to achieve low pressure. The electron source was 15 mm away from the surface of the sample. The magnification at which the photographs were taken is 5000X. FTIR characterizations for (BiVO4)x/CuTl-1223 composites were performed by FTIR spectrophotometer model SHIMADZU-8400S. The traditional four-probe procedure was applied to measure the electrical resistivity for (BiVO4)x/CuTl-1223 composites from room temperature down to the zero superconducting transition temperature (T0) via closed cryogenic cooling system (Displex).

At room temperature, a microhardness tester IN-412A was used to assess the Vickers microindentation of the examined composites in atmospheric air. The applied force was varied from 0.49 to 2.94 N for a loading duration of 10 s, and the indentation diagonals were measured with ± 0.1 μm precision. By obtaining 5 measurements at different positions on the specimen surface, an average value of the microhardness number (Hv) was computed.