The Optimization of Jc, Birr, n value, Wires Diameter, and Research of the Dominant Pinning Mechanism for Applications of Undoped MgB2 in Superconducting Multi-section Coils

This article discusses the influence of MgB2 wire diameter on critical parameters, dominant pinning mechanism, and n value. Studies were conducted on multifilament MgB2 wires of the 0.84 mm and 0.64 mm diameter. The wires were annealed under 1 GPa isostatic pressure, between 650 and 730 °C. Studies show that the best results (Jc, Birr, n value, and point pinning mechanism) for a 0.64-mm wire were obtained with annealing temperature of 650 °C. However, the best results for wires with a 0.84-mm diameter were obtained with annealing temperature of 730 °C. This research was conducted for exploring the use of MgB2 wires in multi-section superconducting coils, e.g., main coils generating magnetic fields and compensation coils—increasing the homogeneity of the magnetic field. Our research indicates that the main coil made with larger diameter wires should be heated at higher temperature (730 °C). In contrast, compensating coils with smaller diameter wires should be heated at a lower temperature (650 °C).


Introduction
Research presented by Uchiyama et al. [1], Wang et al. [2], and Gajda et al. [3] showed that the reduction of the diameter of a superconductor wire as the result of cold drawing led to an increase of critical current density, irreversible magnetic field, pinning force, n value, and dominant pinning mechanism for samples heat treated at a constant temperature, due to increased MgB 2 density, Mg elongation, formation of a layered structure, and increased density of pinning centers [1][2][3][4][5]. In contrast, Xu et al. indicated that a significant reduction of wire diameter causes a decrease of J c [6]. The critical current density, irreversible magnetic field, and dominant pinning mechanism in MgB 2 material depend on many factors, e.g., connections between grains, nano-additives [7,8], the purity of the starting materials [9,10], milling time [9][10][11], type of pinning centers [12][13][14], heat treatment temperature [15], defects, pores, and voids [16]. The n value, which qualifies the transition from the superconducting state to the normal state, is an important factor that influences the selection of the operating current for a superconducting device, coil, magnet, etc. [17]. The n value of a superconductor has a dependency on both intrinsic (connections between grains, grain microstructure, pinning centers) and extrinsic (filament distribution and quantity) [18,19] factors. Superconducting applications include magnetic resonance imaging (MRI), induction furnace, magnetic separation, energy storage, laboratory magnets, and the International Thermonuclear Experimental Reactor. Many of these applications such as MRI require the generation of magnetic fields with high homogeneity produced from the superconductor coil. Unfortunately, superconducting coils have a large magnetic field gradient (difference in magnetic field between the magnet center and the magnet end). This disadvantage is eliminated by external compensating windings, which are coils that significantly increase the homogeneity of the magnetic field in the magnet. Compensation windings are made with superconductor wires of smaller diameter than the superconductor wires used in the main coil windings. Traditional superconducting magnets in the past were made using reacted superconducting wires (superconductive phase). More often today, coils are made with using unreacted wires and tapes such that the superconducting phase will be produced after the wire is wound on the coil former. This method eliminates cracks (e.g., damage to connections between inbound, Nb barriers) which it might occur during winding the coil. One crack significantly reduces J c and hinders the use of the superconducting coil. Usually, the superconductor coils are made of several kilometers of superconducting wires. Based on superconductivity characterization and scanning microscope electron (SEM) analyses, small coil (diameter 14 mm) wounds with unreacted MgB 2 wires have obtained high critical current density when annealed under high isostatic pressure of 1 GPa. In addition, Gajda et al. showed that the HIP process can be applied to small coils with no loss in superconductivity properties as compared with short samples [20]. The HIP process has been demonstrated to improve homogeneity and density of MgB 2 ; reduce pore size, grains, and voids; improve the connection between grains; create pinning centers with homogeneous distribution; and increase the melting point in wires [21][22][23][24]. Moreover, Gajda et al. demonstrated that high isostatic pressure of 1 GPa significantly increased J c in high magnetic fields [3].
This research was conducted to determine the impact of MgB 2 wire diameter and high isostatic pressure heat treatment on J c , B irr , n value, F p , dominant pinning mechanism, and MgB 2 material structure. The goal was to identify the optimal heat treatment protocol for the production of multi-sectional superconducting MgB 2 coils.

Preparation of Samples
The in situ MgB 2 wires were made of powders with purity of 99% (the nominal atomic ratio 1.10:2) and average boron and magnesium powder size of 50 nm and 40 μm. The filaments are made with continuous tube forming and filling (CTFF) method and restacked as a 18-filament wire at Hyper Tech Research, Inc. [25]. The wire compositions were Nb chemical barrier, Cu filamentary matrix, and Monel outer sheath; the fill factor was 15%, and the wires were drawn to 0.64 and 0.84 mm. The wires of both sizes were heat treated together at the same temperature (from 650 to 730°C), pressure (1 GPa), and time (from 15 to 60 min) at the Institute of High Pressure Physics in Warsaw (see Table 1) [26,27]. Critical current measurements were made at the Institute of Low Temperature and Structure Research PAS in Wroclaw, with a four-probe resistive method. All samples were measured in a perpendicular magnetic field (Bitter-type magnet-14 T) at liquid helium temperature, with constant current, and in accordance with a 1 μV/cm criterion [28]. Sample length was 20 mm. Kramer analysis used the J c 0.5 *B 0.25 formula [29]; scaling used the k*(h p )*(1-h) q formula [30]. Analysis of the microstructure and composition were performed by FEI Nova Nano 230 SEM at the Institute of Structural Research and Low Temperatures PAS in Wroclaw.

SEM Analysis
The results in Fig. 1 show the cross (Fig. 1a, b, e, f) and longitudinal ( Fig. 1i and j) sections for sample A and B. Sample B has better connection between particles than sample A. In sample B, the small number of small-sized voids is created. In Fig. 1 we see cross (Fig. 1c, d, g, h) and longitudinal ( Fig. 1k and l) sections for sample G and H. These photos indicate the larger and more voids are formed in sample H compared with sample G. This leads to the reduction of the density, homogeneity, and number of grains connections in the sample H. This leads to the reduction of the transport critical parameters in the superconducting materials. Based on the results in Fig. 1, it can be concluded that the synthesis reaction is faster in the of 0.64-mm-diameter wires than 0.84 mm diameter wires. The MgB 2 wires of the 0.64 mm diameter are obtained with the MgB 2 wires of 0.84 mm diameter by using cold drawing. Susner et al. showed that cold drawing causes elongates and reduces the thickness of Mg grains [5]. This leads to the faster synthesis reaction rate in MgB 2 wires of the 0.64 mm diameter.

Annealing Temperature (T a ) of 650°C for 60 min
The measurements and calculations indicate that a reduction of the MgB 2 wire diameter from 0.84 to 0.64 mm significantly increases J c in sample B (1000 A/mm 2 in 6.3 T and 100 A/ mm 2 in 10 T) as compared with sample A (1000 A/mm 2 in 5 T and 100 A/mm 2 in 8.5 T). The J c of sample B overall is 50% higher than J c sample A (Fig. 2a). Comparing these results (sample B) with the results of Li et al. [31] and Yamada et al. [32], our undoped MgB 2 wires have higher J c than undoped MgB 2 wires studies by others (1000 A/mm 2 in 3 T and 100 A/mm 2 in 6.2 T-annealing temperature of 675°C) [31] and tapes (500 A/mm 2 in 7 T and 100 A/mm 2 in 9.5 Tannealing temperature of 630°C) [32]. The maximum pinning force (F pmax ) is in 4 T (6400 MN/m 3 ) for sample A and 5 T (8700 MN/m 3 ) for sample A, Fig. 2b. The 5 T F pmax is a good result for undoped MgB 2 wires. Based on Kramer [29], the irreversible magnetic field (B irr ) was 15.2 T for sample A and 16.3 T for sample B (Fig. 3). Analysis of Dew-Hughes in Fig. 4 shows that for sample A, F p /F pmax equals 1 is in B/ B irr = 0.27, meaning that point dominant pinning mechanism is in ranges from 0 to 0.27, shifting first to surface pinning and then to volume above 0.27. For sample B, F p /F pmax equals 1 is in B/B irr = 0.32 ( Fig. 4), showing that point dominant pinning mechanism is in ranges from 0 to 0.32 and above 0.32 dominant pinning mechanism shifts first to surface and then to volume. Based on SEM images ( Fig. 1), we can conclude that Mg grains of smaller thickness correspond to higher J c for reaction heat treatments at low temperatures (650°C).
Critical current density, magnetic field dependency, and n value all are important parameters of a superconductor for the design of coil or magnet using them. The n value parameter describes the quality of the transition of the superconducting   In addition, n value influences the selection of the operating current for designing a superconducting coil [17]. In this paper, engineering critical current density (J ec ) is the critical current density (J c ) divided by the cross-sectional area of the wire. Currently, applications of superconducting wire should have the engineering critical current density of about 100 A/ mm 2 and n value of 20 [17]. Measured n values for sample A and B is shown in Fig. 5. Sample A annealed at 650°C for 60 min with 1 GPa pressure obtained an n value of 20 and J c of 1600 A/mm 2 (240 A/mm 2 J ec ) at 4 T; sample B annealed with the same parameters had a n value of 20 and J c of 1260 A/mm 2 (J ec -318 A/mm 2 J e ) at 6 T. Parizh et al. indicated that for n value of 20, the operating current of a superconducting coil would be set to 50% of the critical current [17]. Figure 5 shows the dependencies of n value with both current density J c and applied field B. The relationship between n value and B indicates that the reduction of the MgB 2 wire diameter significantly increases n value in low and middle magnetic fields. It should be recalled that critical current density depends on pinning center density and that the pinning centers are activated by the external magnetic field [14]. Gajda et al. indicated that different types of pinning centers strongly pin the vortex lattice in different ranges of magnetic field [33]. Calculations carried out using the CMF [34] method for sample B with an n value of 20 indicate that the B/B irr (6 T/16.5 T) coefficient is 0.36. This B/B irr coefficient value indicates dominant point pinning centers. On the other hand, calculations for sample C show that the B/B irr coefficient is 0.26 for an n value of 20, meaning that dominant mechanism is surface pinning. Dew-Hughes analysis shows that the reduction of the wire diameter leads to the change of the dominant pinning mechanism. On this basis, it can be deduced that the n value increase in a MgB 2 wire with sized to 0.64 mm was a result of a high density of point pinning centers being obtained.
The n value-J c relationship indicates that the reduction of the MgB 2 wire diameter does not influence n value. This indicates that the same pinning force (F p ) is present in both samples A and B. However, Dew-Hughes, SEM, and CMF analysis [34] indicate that the J c in sample B was created by  Figure 6a, c, and e show that an increase of annealing temperature from 680 to 730°C in MgB 2 wires with a 0.84 mm diameter increases J c by 50%. SEM results in Fig. 1 indicate that the higher annealing temperature (730°C) of undoped MgB 2 wires with a diameter of 0.84 mm produces a greater number of big and small voids (point and surface pinning centers) and increases the number of connections between grains. Therefore, the J c for 0.84-mm-undoped MgB 2 wires increases with increased annealing temperature. On the other hand, increasing the annealing temperature from 680 to 700°C in 0.64-mm MgB 2 wires reduces J c by 40%. Increasing the annealing temperature further to 730°C decreases J c by 25% between 2 and 8 T and increases J c by 25% above 8 T (Fig. 7). SEM pictures show that annealing at 730°C of wires with a 0.64 mm diameter creates big voids, creating surface pinning centers and reducing the number of connections between grains, leading to a decrease in J c . The improvement of J c above 8 T in sample H indicates that the annealing temperature of 730°C led to formation of high-field pinning centers, creating dislocations and strains. At 730°C and 1 GPa, Mg is in a liquid state and B solid state. Large voids (Fig. 1) and strains (dislocations) are created, while Mg is in the liquid state. Increasing annealing from 680 to 730°C for 0.84-mm wires significantly increases F p in low and middle magnetic fields (Fig. 6b, d, and f), suggesting that the higher annealing temperature increased the number of surface and point pinning centers. In Fig. 6b, d, and f, increasing annealing from 680 to 730°C for 0.64-mm wires significantly decreases F p in low and middle magnetic fields and shifts F pmax from 4 to 2.5 T, suggesting that the higher annealing temperature decreased the number of point pinning centers. The Kramer analysis [29] showed that increasing annealing from 680 to 730°C in 0.84-mm wires increases B irr from 15.9 to 16.3 T and decreases B irr from 16.5 to 15.2 T in 0.64-mm wires. The B irr depends on the type and density of high-field pinning centers. In superconducting material, there are three types of high-field pining centers, e.g., dislocations, strains (e.g., substitution for C by B), and intra-grain precipitation [14]. Serquis et al. [21] showed that HIP process formed dislocations. This indicates that in our undoped MgB 2 wires thermally treated under 1 GPa isostatic pressure, it mainly forms high-field pinning centers. On this basis, we can indicate that increase of the annealing temperature from 680 to 730°C and the isostatic pressure of 1 GPa allows to increase the density of high-field pinning centers in undoped MgB 2 wires of 0.84 mm diameter. However, an increase of the annealing temperature and the isostatic pressure of 1 GPa leads to a decrease in the density of high-field pinning centers in undoped MgB 2 wires of the 0.64 mm diameter.

Annealing Temperature (T a ) from 680 to 730°C by 15 min
This same increase of annealing temperature for 0.64-mm wires causes a shift of maximum ratio F p /F pmax = 1 from B/ B irr = 0.25 (680°C) to 0.16 (730°C) (Fig. 8), indicating that the increase of annealing temperature changes the dominant pinning mechanism from surface to volume (big voids) (Fig.  1). Our calculations and extrapolations for 0.84-mm-undoped MgB 2 wire shows that these wires also have the surface dominant pinning mechanism. A longer annealing time (60 min), 700°C annealing temperature, and 1 GPa isostatic pressure reduces J c (e.g., 100 A/mm 2 at 8.8 T for 0.84-mm wire and 100 A/mm 2 at 7.2 T for 0.64 mm) (Fig. 9). Therefore, further studies with longer annealing time (e.g., 60 min) were not conducted for 700°C and 1 GPa isostatic pressure.
The dependency of n value with B in Fig. 10 shows that increasing the annealing temperature from 700 to 730°C for 0.84-mm-undoped MgB 2 wires n value increases, e.g., to 30 at 700°C, 5 T and 1129 A/mm 2 (J ec -170 A/mm 2 ), and to 45 at 730°C, 5 T and 1407 A/mm 2 (J ec -211 A/mm 2 ). The results for sample F (0.64 mm) show that higher annealing temperature corresponded to a low n value (of 9 at 5 T and 750 A/mm 2 (J ec -100 A/mm 2 )), indicating that wire diameter reduction, high annealing temperature, and 1 GPa high isostatic pressure significantly reduces n value. In Fig. 10 we see the reduction of wire diameter and high annealing temperature (700°C) significantly reduces n value, e.g., sample E has n value of 50 at 1700 A/mm 2 J c , and sample F has n value of 20 at 1700 A/mm 2 J c . On the other hand, higher annealing temperature for 0.84-mm wires increases the n value, e.g., sample G has n value of 28 at 1000 A/mm 2 J c (150 A/mm 2 J ec ) and sample G has n value of 35 at 1000 A/mm 2 J c . Previously results indicated that J c is dependent on the density of the  Fig. 5 The n value dependence of the two specified wires diameters obtained for the perpendicular to the wires axis magnetic field in undoped MgB 2 wires pinning centers and that the pinning centers activate the external magnetic field [14]. Based on these assumptions, Dew-Hughes analysis and CMF method [34], it can be concluded that increasing the annealing temperature from 680 to 730°C for 0.64-mm wires increases the surface pinning centers density and decreases the point pinning centers density, e.g., sample F with an n value of 20 has a B/B irr coefficient (3 T/15 T) of 0.2-this value indicates surface pinning [34], leading to a reduction of J c and n value. For 0.84-mm wire samples, increasing the annealing temperature creates a higher density of point pinning centers, e.g., sample E has B/B irr coefficient of 0.38 with an n value of 20-this value indicates point pinning centers, which correspondingly increases J c and n value. Based on the results above, multi-sectional wind-and-react coils cannot be fabricated with wires of two different diameters. For example, a low annealing temperature of the coil would produce high current density and n value in the compensating coil windings and low critical current density and n value in the main coil. On the other hand, a high annealing temperature would produce high critical current density and n value in the main coil and low critical current density and n value in the compensation coil. In both cases a homogeneous distribution of the magnetic field in the coil would not be realized. We suggest a better method for fabricating multisectional superconducting coils. First the main coil made would be fabricated with unreacted wires of large diameter and annealed at a high temperature for producing high J c and n value. Secondly, the compensating windings would be wound to the main coil and the combined coil set. These combined coil set will heat treated at a low temperature (e.g. 570°C [35]) for producing high J c and n value in the compensation coils. The low annealing temperature would not   Fig. 9 Transport J c -B curves for undoped MgB 2 wires in perpendicular magnetic field for 700°C by 60 min under 1 GPa adversely affect the critical parameters of the main coil, because the already-formed ex situ MgB 2 material has the high melting point above 900°C [36].

The Conclusions
Our research shows that the rate of reaction in undoped MgB 2 wires with 0.64 mm diameter is faster than the reaction rate in undoped MgB 2 wires with 0.84 mm diameter. The faster reaction rates are associated with thinner Mg grains and high isostatic pressure during heat treatment. Moreover, low annealing temperatures (650°C) for 0.64-mm wire, high isostatic pressure, and long annealing time (60 min) yield smaller grains and voids and an increased number of connection between grains, high MgB 2 material density, very high J c of 1000 A/mm 2 at 6 T, J ec of 100 A/mm 2 at 7 T, B irr , F p high n values, and point dominant pinning mechanism. On the other hand, high annealing temperature (730°C) with high pressure and short annealing time (15 min) produces large grains and voids; reduces the number of connections between grains; reduces the uniformity and density of the MgB 2 material; and decreases J c (1000 A/mm 2 at 4 T with J ec of 100 A/mm 2 at 5 T), n value, F p , B irr , and surface dominant pinning mechanism. Critical parameters including n value are reduced in 0.84-mm wires with low annealing temperature and high isostatic pressure. However, a high annealing temperature significantly increases the critical parameters of MgB 2 wires sized to 0.84 mm, suggesting that for the manufacturing of multisectional superconducting coils, the main coil should be fabricated first and should be annealed at a high temperature. The compensation coil would be fabricated after the main coil and heat treated at a low temperature, which will allow to maintain high magnetic field in both main and compensation coils. This coil manufacturing process will lead to improvements in the homogeneity of the magnetic field in multi-sectional coils. Our analysis of the relationship of n value with J c and B showed that n value is significantly dependent on the type of pinning centers. Point pinning centers significantly increased n value in middle magnetic fields, whereas surface pinning centers significantly increased n value in low magnetic fields.
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