1 Introduction

MgB2 superconductor is considered to be the most promising candidate for cryogen-free operation for the last two decades. Intensive studies held over experimental and theoretical aspects of the MgB2 superconductor since discovery in 2001 [1]. MgB2is important because of its simple crystal structure, low material coast, relatively high transition temperature (T C ), large coherence length, and transparency of grain boundaries to current flow [2]. However, MgB2 superconductor still needs to improve its upper critical current (H c2), critical current density (J c ) for the practical applications to replace the conventional Nb-Ti and Nb-Sn superconductors. However, low pinning strength causes a rapid drop in J c in high magnetic fields [3]. Various kinds of techniques such as chemical doping [3–12], irradiation [13, 14], and thermo-mechanical processing techniques [15–18] have been employed to overcome this issue. Planetary ball milling is extensively used for mixing the constituent materials in the preparation of the MgB2 samples because of its ease of use, flexibility and scalability [19–25]. The uniform dispersion of a small amount of the nano materials is the key issue in achieving the optimum effect of the dopant on the physical properties of MgB2. The uniform dispersion of the dopant by planetary BM depends on more than one parameter such as time, rotation per minute (rpm), ratio of numbers of ball, and amount of the materials. The higher rpm causes the oxidation of Mg due to heat generated during milling. Thus, this restricts the higher rpm. There is a need to optimize these BM time parameters keeping low rpm to achieve the uniform dispersion of the very small amount of the dopant. In the present work, the effect of BM time during the mixing of the constituent materials on the doping of glucose and hence the structural, electrical, and magnetic properties of MgB2 superconductor is investigated in details. The quantification of the dispersion of glucose in MgB2 is reported earlier by our groups [26]. In the present study, we kept the percentage of doping of glucose such that it gives 2 atomic % of C in Mg (B 1−XC X )2. Four different samples of 2 % glucose were prepared by varying the ball milling time from 2 to 12 h. A pure MgB2 reference sample with 8 h of ball milling was also prepared for comparison. The XRD, resistivity, and magnetization measurements were carried out for all the samples. In comparison to all samples the 8h ballmilled 2 % glucosedoped sample shows the excellent Jc-H and Hirr

Fig. 1
figure 1

XRD pattern of 2 % glucose-doped MgB2 for different ball milling times

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2 Experimental Details

In this work, the glucose-doped MgB2 samples were prepared by in situ solid-state reaction method. The constituent materials were 99.99 % crystalline boron powder (Sigma Aldrich), 99.9 % Mg powder (CERAC with an average particle size of 45 μm), and 99.9 % glucose, C6H12O6,(Fluke). These were mixed in stoichiometric ratio using planetary ball milling machine. The constituent materials were weighed and ball milled for 2, 4, 8, and 12 h, respectively, in an 80-ml Zr2O bowl using six 1-cm diameter ball of Zr2O at a 100-rpm speed. These are henceforth termed as 2-, 4-, 8-, and 12-h samples. The details are described in elsewhere [26].

XRD measurement was done on PANalytical X’Pert Pro MPD X-ray Diffractometer using Cu K α radiation. Resistivity measurements from room temperature (RT) to 30 K were carried out using an in-house standard four-probe technique fitted to APD closed cycle cryo-cooler. The critical current density was calculated from M-H loop measured by 14T physical property measurement system (PPMS; Quantum Design). The ac susceptibility measurement as a function of temperature was done using an in-house ac susceptometer [27].

3 Results and Discussion

The XRD clearly depicts that the major phase is MgB2 and a small impurity phases of MgO is unavoidable. The very small amount of unreacted Mg is also present which gets diminished with an increase in ball milling time, whereas the MgO amount increases. This is due to the decrease in the average particle size of Mg, which leads to an increase in reactive surface area and a uniform dispersion of the particle [26]. The lattice parameters a and c are shown in Fig. 2. The reference sample, pure one, has a–lattice parameter 3.086 Å. In doped samples, the value of a decreases from 3.085 to 3.070 Å with an increase in BM time and gets saturated around 8 h. However, the c-lattice parameter remains nearly constant as a function of BM time. This decrease in a-lattice parameter and approximately constant c value is an indication of the substitution of C in the B plane of MgB2 lattice. It has been argued that the doping causes lattice distortion and increase in the lattice strain which is the cause of the decrease in the a-lattice parameters not the substitution. To verify this, we calculated the lattice strain and crystallite size using the Williamson and Hall model [28];

$$\text{FWHM}\times \cos {\theta = \frac{0.94\lambda}{(\mathrm{Grain\,\,size})}} +4 \times \text{strain} \times \sin \theta $$
Fig. 2
figure 2

Variation of lattice parameter a, c of 2 % glucose-doped, and pure samples as a function of ball milling time

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Where FWHM is full widths at half maxima of XRD peaks and λ is the wavelength of CuKα radiation (1.540598 A0). The strain and particle size as a function of ball milling time is plotted in Fig. 3a, b. From the graph, it is clear that the strain in the lattice remains constant up to 8 h of BM time. Thus, a decrease in the a-lattice parameter in the present case is due to the substitution of more and more C in the lattice with increasing BM time. Thus, a minimum BM time of 8 h is necessary to disperse the glucose uniformly in the present case. But more increase in the BM time does not affect the dispersion rather degrade the samples due to the formation of more and more MgO which is evident from the XRD. From the figure, it is clear that the increase in BM time reduces the formation of crystallite size. As we increase the BM time, the glucose gets dispersed uniformly and B gets coated with C source. At the time of sintering, the C inhibits the formation of a larger crystallite of MgB2. Thus, the reduction in crystallite size is due to the increase in the uniformity of glucose in starting materials and coating of the B crystallite uniformly and hence the uniform dispersion of the C in the MgB2 lattice as BM time increases. This phenomenon gets saturated after 8 h. The 8 h is the optimum time for the uniform mixing of glucose.

Fig. 3
figure 3

a Strain versus BMT, b particle size versus BMT, c transition temperature versus BMT, d the effective area of current carrying fraction (A f ) versus BMT, and e ΔT c versus BMT

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The transition temperature (T C ) measured from resistivity and susceptibility both shows the decrease of it from 38.3 to 37.4 K with ball milling time (see Fig. 3c). This decrease in transition temperature can be related to the substitution of carbon in boron plane by better dispersion of the dopant. The effective area of current-carrying fraction (A f ) is estimated from the Rowell criteria [29] (see Fig. 3d), where \(Af=^{\Delta \rho _{\text {ideal}}}\) Δρ with Δρ ideal = 7.3μΩ cm and Δρ = ρ(300K)−ρ(40K). It is clear from the figure that the effective current-carrying area fraction decreased from 10.8 to 7.2 % with an increase in ball milling. This might be due to increase in the formation of MgO phase with the increase in BM time which has been observed in XRD pattern.

The critical current density J C (H,T) of all samples was calculated from the M-H loop measurements, using the Bean model. Figure 4 shows the Jc-H curves at 5 and 20 K for the samples studied in this work. At 5 K, J C of 104 A/cm2 value in 8.2T and at 20 K, the J C value of 104 A/cm2 in 4T has been achieved in an 8-h ball milled. At both temperatures, the Jc(H,T) behaviors are significantly improved by increase in ball milling time. It is found that the sample ball milled for 8 h gets the best result in high field region. The excellent performance of 8-h ball-milled samples is due to the maximum and uniform substitution of C in the MgB2 lattice discussed above. The substitution causes the increase in H c2 and hence increase in the J c in higher field. The further increase in ball milling decreased the Jc(H,T) performance, it is due to the excess formation of MgO phase and decrease in the superconducting volume. This is very much clear from the ac susceptibility studies as shown in Fig. 5 in which a 12-h ball-milled sample shows two peaks in imaginary parts and two steps in the real part of ac susceptibility.

Fig. 4
figure 4

Critical current density (Jc) measured at 5 and 20 K for the applied field of up to 13T

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Fig. 5
figure 5

Real and imaginary parts of ac susceptibility (χ) as a function of temperature (K)

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The degradation of J c in the low field as a function of BMT is obvious. This has been observed in all C-doped samples. Here, we observe a decrease in the A f as a function of BM time. One of the causes of the degradation of low field J c is the decrease in the effective area and other is due to a decrease in the pinning force in the C-doped samples at the lower field [30].

4 Conclusion

In summary, structural analysis has been performed on the samples with different ball milling time. The reduction in a−lattice parameter indicates the substitution of boron by carbon in MgB2 matrix. The strain and particle size were calculated from XRD using Williamson Hall plots. The strain remains constant while the particle size decreased with the increase in the ball milling time. Systematic decrease in transition temperature and a-lattice parameters as a function of BM time and saturation of it at an 8-h BM time clearly indicates that the optimum dispersion of glucose and hence the uniform substitution of C in the MgB2 lattice is achieved at 8 h of BM time. Therefore, we get the highest J C (H,T) performance in the 8-h BM samples. However, a further increase in BM time degrades the samples due to the increase in the MgO phase formation beyond certain limits. This is evident from the XRD study and ac susceptibility measurement of a 12-h sample. Thus, we conclude that optimum BM time is necessary to disperse the small amount of glucose uniformly inside the MgB2 lattice to get the maximum benefit of dopants.