The Influence of Preparation Temperature on the Different Facets of Bulk MgB2 Superconductors

Two MgB2 samples were prepared using the spark plasma sintering (SPS) technique at different temperatures—950 °C (S1) and 975 °C (S2)—for 2 h under 50 MPa pressure to study the influence of preparation temperature on different facets, namely those perpendicular (PeF) and parallel (PaF) to the compression direction of uniaxial pressure during the SPS of MgB2 samples. We analyzed the superconducting properties of the PeF and PaF of two MgB2 samples prepared at different temperatures from the curves of the critical temperature (TC), the curves of critical current density (JC), the microstructures of MgB2 samples, and the crystal size from SEM. The values of the onset of the critical transition temperature, Tc,onset, were around 37.5 K and the transition widths were about 1 K, which indicates that the two samples exhibit good crystallinity and homogeneity. The PeF of the SPSed samples exhibited slightly higher JC compared with that of the PaF of the SPSed samples over the whole magnetic field. The values of the pinning force related to parameters h0 and Kn of the PeF were lower than those of the PaF, except for Kn of the PeF of S1, which means that the PeF has a stronger GBP than the PaF. In low field, the most outstanding performance was S1-PeF, whose critical current density (JC) was 503 kA/cm2 self-field at 10 K, and its crystal size was the smallest (0.24 µm) among all the tested samples, which is consistent with the theory that a smaller crystal size can improve the JC of MgB2. However, in high field, S2-PeF had the highest JC value, which is related to the pinning mechanism and can be explained by grain boundary pinning (GBP). With an increase in preparation temperature, S2 showed a slightly stronger anisotropy of properties. In addition, with an increase in temperature, point pinning becomes stronger to form effective pinning centers, leading to a higher JC.


Introduction
Since Akimitsu [1] discovered the superconductivity of MgB 2 , it had been studied extensively by scientists from all over the world [2], and researchers have processed MgB 2 into tapes, wires [3], films [2,4], and bulks based on in situ and ex situ methods [5]. Compared to low-temperature superconductors, MgB 2 has a higher critical temperature (T C ) and a higher critical current density (J C ) [6][7][8]. However, it has a lower coherence length, lower anisotropy, and a good grain boundary connection compared with high-temperature superconductors [9]. More important is that its raw materials, magnesium and boron, are abundant on Earth [10], which means that its preparation is much less expensive than that of REBa 2 Cu 3 O 7-x (RE represents a rare Earth element, such as Gd, Nd, Sm, etc.) bulk superconductors [11][12][13]. It is also speculated that, according to the raw materials of MgB 2 superconducting bulks, there are no toxic elements in their ingredients, which is relatively

Experimental Section
Grade A magnesium diboride from ABCR GmbH (Karlsruhe, Germany) was used as the starting powder and then loaded into a graphite die and processed using the spark plasma sintering technique (FCT System GmbH, HD25, Rauenstein, Germany) in DC mode. A pulsed electric current (2000 A, 4 V) was passed through the sample under a dynamic vacuum (10 −3 bar) while a 50-MPa uniaxial pressure was applied [22]. In this study, two SPSed bulk samples with disc shapes 20 mm in diameter and 3 mm in thickness were fabricated at different temperatures-950 • C (S1) and 975 • C (S2)-for 2 h under a pressure of 50 MPa.
To study the effect of preparation temperature on the performance of MgB 2 bulks, small specimens of rectangular shape positioned beneath the edge of MgB 2 bulk samples were cut into sizes of 2 mm × 2 mm × 1 mm from these bulk samples for the measurement of superconducting properties, as shown in Figure 1. The phase position and lattice parameters were confirmed using X-ray diffraction (XRD) at room temperature. Scanning electron microscopy (SEM, microscope model, company, city, country)) was used to observe the microstructure of these samples, and the crystal size of the SPSed MgB 2 was calculated according to the SEM using Nano Measurer 1.2. The element analysis was conducted using energy-dispersive X-ray spectroscopy (EDS). The DC magnetization measurement was measured using a Quantum Design SQUID magnetometer under a magnetic field perpendicular to the tested facet for the superconducting transition and magnetic hysteresis loops of MgB 2 samples. The values of critical current density (J C ) were calculated based on the extended Bean's critical state model [16,26]. The facets perpendicular to the compression direction in the SPS process were marked as perpendicular facets (PeF), and the facets parallel to the compression direction were marked as parallel facets (PaF). The two kinds of facets were compared to study the differences in superconducting properties between the PeF and PaF.
Micromachines 2023, 14,988 3 of 12 perpendicular to the compression direction in the SPS process were marked as perpendicular facets (PeF), and the facets parallel to the compression direction were marked as parallel facets (PaF). The two kinds of facets were compared to study the differences in superconducting properties between the PeF and PaF.

Superconducting Properties of the PeF and PaF of MgB2 Samples at Different Preparation
Temperatures (950 °C and 975 °C) Figure 2 shows the room-temperature XRD patterns of samples prepared at 50 MPa uniaxial pressure and different temperatures, 950 °C (S1) and 975 °C (S2), using spark plasma sintering technology. It can be seen from Figure 2 that the main component of the samples is MgB2, although there are a few second phases, such as MgB4 and MgO.
The oxidation reaction appears under the oxygen condition during growth [21,27]. High temperature and pressure conditions during the process [27,28] may result in the generation of MgB4. These kinds of particles may have an important effect on the superconducting properties of SPSed samples. Room-temperature X-ray diffraction patterns of samples prepared using the spark plasma sintering method at 950 °C (S1) and 975 °C (S2) for 2 h under 50 MPa pressure.
The standard lattice parameter values of MgB2 without doping any other substances are a = 3.086 Å, c = 3.524 Å. Table 1 shows that the lattice parameters of the samples at different temperatures, 950 °C (S1) and 975 °C (S2), are a = 3.0847 Å, 3.0811 Å, c = 3.5232 Å, and 3.5223 Å, respectively. A small a-axis lattice parameter is reflected in the substitution of carbon from the graphite mold system for boron in the crystal lattice of MgB2 during the process [29,30]. The lattice parameters of S1 are closer to the standard values   Figure 2 shows the room-temperature XRD patterns of samples prepared at 50 MPa uniaxial pressure and different temperatures, 950 • C (S1) and 975 • C (S2), using spark plasma sintering technology. It can be seen from Figure 2 that the main component of the samples is MgB 2 , although there are a few second phases, such as MgB 4 and MgO.
The oxidation reaction appears under the oxygen condition during growth [21,27]. High temperature and pressure conditions during the process [27,28] may result in the generation of MgB 4 . These kinds of particles may have an important effect on the superconducting properties of SPSed samples. perpendicular to the compression direction in the SPS process were marked as perpendicular facets (PeF), and the facets parallel to the compression direction were marked as parallel facets (PaF). The two kinds of facets were compared to study the differences in superconducting properties between the PeF and PaF.  Figure 2 shows the room-temperature XRD patterns of samples prepared at 50 MPa uniaxial pressure and different temperatures, 950 °C (S1) and 975 °C (S2), using spark plasma sintering technology. It can be seen from Figure 2 that the main component of the samples is MgB2, although there are a few second phases, such as MgB4 and MgO.

Superconducting Properties of the PeF and PaF of MgB2 Samples at Different Preparation Temperatures (950 °C and 975 °C)
The oxidation reaction appears under the oxygen condition during growth [21,27]. High temperature and pressure conditions during the process [27,28] may result in the generation of MgB4. These kinds of particles may have an important effect on the superconducting properties of SPSed samples. The standard lattice parameter values of MgB2 without doping any other substances are a = 3.086 Å, c = 3.524 Å. Table 1 shows that the lattice parameters of the samples at different temperatures, 950 °C (S1) and 975 °C (S2), are a = 3.0847 Å, 3.0811 Å, c = 3.5232 Å, and 3.5223 Å, respectively. A small a-axis lattice parameter is reflected in the substitution of carbon from the graphite mold system for boron in the crystal lattice of MgB2 during the process [29,30]. The lattice parameters of S1 are closer to the standard values The standard lattice parameter values of MgB 2 without doping any other substances are a = 3.086 Å, c = 3.524 Å. Table 1 shows that the lattice parameters of the samples at different temperatures, 950 • C (S1) and 975 • C (S2), are a = 3.0847 Å, 3.0811 Å, c = 3.5232 Å, and 3.5223 Å, respectively. A small a-axis lattice parameter is reflected in the substitution of carbon from the graphite mold system for boron in the crystal lattice of MgB 2 during the process [29,30]. The lattice parameters of S1 are closer to the standard values of MgB 2 . Therefore, we can infer that the performance of the S1 sample may be slightly better than that of the S2 sample.  Figure 3 shows the sample temperature dependence of magnetization curves of MgB 2 samples prepared at different temperatures of 950 • C (S1) and 975 • C (S2) for 2 h under 50 MPa pressure. The onset of the critical transition temperature, T c,onset , is at around 37.5 K and the transition width is about 1 K, which indicates the two samples exhibit good crystallinity and homogeneity. The T c,onset of S1 is slightly higher than that of the S2 sample, which may be related to the good performance of the S1 sample. of MgB2. Therefore, we can infer that the performance of the S1 sample may be slightly better than that of the S2 sample.  Figure 3 shows the sample temperature dependence of magnetization curves of MgB2 samples prepared at different temperatures of 950 °C (S1) and 975 °C (S2) for 2 h under 50 MPa pressure. The onset of the critical transition temperature, Tc,onset, is at around 37.5 K and the transition width is about 1 K, which indicates the two samples exhibit good crystallinity and homogeneity. The Tc,onset of S1 is slightly higher than that of the S2 sample, which may be related to the good performance of the S1 sample.  Figure 4 shows the curves of the magnetic field and JC from different facets (PeF and PaF) measured at 20 K, and the embedded diagram shows their self-field JC at different preparation temperatures. It can be seen that JC decreases with the increase in the magnetic field. The PeF of the SPSed samples exhibits a slightly higher JC compared with that of the PaF of the SPSed samples in the whole magnetic field. In the low magnetic field, the highest self-field JC is 342 kA/cm 2 in the S1-PeF samples, as shown in Figure 4. The self-field JC of the S2-PeF sample is 333 kA/cm 2 . The self-field of JC in the PaF of the S1 and S2 samples is 326 kA/cm 2 and 317 kA/cm 2 , respectively. In the high magnetic field, the increase of JC appears in the PeF of S2 samples, which is important for the future application of MgB2 bulks. It is clear that the PeF and PaF of S1 processed under lower prepared temperatures possess the optimum superconducting performance in a low magnetic field; however, JC of the PeF of the S2 sample processed under higher prepared temperatures is more advantageous in a high magnetic field, which indicates that the preparation temperatures (950 °C and 975 °C) of the samples are appropriate. According to the report [5], the superconductor bulks MgB2 prepared at a temperature of 850 °C with the ex situ method using the SPS technique show the best JC in the whole magnetic field compared with the bulks prepared at different temperatures. The value of JC increases first and decreases then with the increase in the preparation temperature to 800  Figure 4 shows the curves of the magnetic field and J C from different facets (PeF and PaF) measured at 20 K, and the embedded diagram shows their self-field J C at different preparation temperatures. It can be seen that J C decreases with the increase in the magnetic field. The PeF of the SPSed samples exhibits a slightly higher J C compared with that of the PaF of the SPSed samples in the whole magnetic field. In the low magnetic field, the highest self-field J C is 342 kA/cm 2 in the S1-PeF samples, as shown in Figure 4. The self-field J C of the S2-PeF sample is 333 kA/cm 2 . The self-field of J C in the PaF of the S1 and S2 samples is 326 kA/cm 2 and 317 kA/cm 2 , respectively. In the high magnetic field, the increase of J C appears in the PeF of S2 samples, which is important for the future application of MgB 2 bulks. It is clear that the PeF and PaF of S1 processed under lower prepared temperatures possess the optimum superconducting performance in a low magnetic field; however, J C of the PeF of the S2 sample processed under higher prepared temperatures is more advantageous in a high magnetic field, which indicates that the preparation temperatures (950 • C and 975 • C) of the samples are appropriate. According to the report [5], the superconductor bulks MgB 2 prepared at a temperature of 850 • C with the ex situ method using the SPS technique show the best J C in the whole magnetic field compared with the bulks prepared at different temperatures. The value of J C increases first and decreases then with the increase in the preparation temperature to 800 • C, 850 • C, 900 • C and 1000 • C, which further suggests that a suitable preparation temperature may exhibit a better superconducting property. Thus, it cannot be fully proved that a higher preparation temperature is harmful to the superconducting properties of MgB 2 bulk in our work; further study, with a wider preparation temperature range, is required. °C, 850 °C, 900 °C and 1000 °C, which further suggests that a suitable preparation temperature may exhibit a better superconducting property. Thus, it cannot be fully proved that a higher preparation temperature is harmful to the superconducting properties of MgB2 bulk in our work; further study, with a wider preparation temperature range, is required. JC of the two samples at the different processed temperatures as a function of the applied field is given in Figure 5. In addition, the embedded diagram shows their irreversible field, represented by μ0Hirr, which is defined as the field when JC reaches 100 A/cm 2 , under different processed temperatures. It is clear that the JC of the S1-PeF possesses the highest JC in a low magnetic field, and the S2-PeF enhances the JC in a high magnetic field, accompanied by the highest μ0Hirr at 20 K. The significant enhancement of JC at a temperature of 10 K appears in a high magnetic field, which will be beneficial to future applications of MgB2 bulks. J C of the two samples at the different processed temperatures as a function of the applied field is given in Figure 5. In addition, the embedded diagram shows their irreversible field, represented by µ 0 H irr , which is defined as the field when J C reaches 100 A/cm 2 , under different processed temperatures. It is clear that the J C of the S1-PeF possesses the highest J C in a low magnetic field, and the S2-PeF enhances the J C in a high magnetic field, accompanied by the highest µ 0 H irr at 20 K. The significant enhancement of J C at a temperature of 10 K appears in a high magnetic field, which will be beneficial to future applications of MgB 2 bulks. °C, 850 °C, 900 °C and 1000 °C, which further suggests that a suitable preparation temperature may exhibit a better superconducting property. Thus, it cannot be fully proved that a higher preparation temperature is harmful to the superconducting properties of MgB2 bulk in our work; further study, with a wider preparation temperature range, is required. JC of the two samples at the different processed temperatures as a function of the applied field is given in Figure 5. In addition, the embedded diagram shows their irreversible field, represented by μ0Hirr, which is defined as the field when JC reaches 100 A/cm 2 , under different processed temperatures. It is clear that the JC of the S1-PeF possesses the highest JC in a low magnetic field, and the S2-PeF enhances the JC in a high magnetic field, accompanied by the highest μ0Hirr at 20 K. The significant enhancement of JC at a temperature of 10 K appears in a high magnetic field, which will be beneficial to future applications of MgB2 bulks.  Figure 6 shows a SEM diagram of the PaF (left) and PeF (right) of the SPSed samples. It is found that some large and white round and oval particles appear in the PaF of both samples, which are oxidative metamorphic MgB 2 grains or MgO secondary particles [7,8]. It has been shown that the size of the effective pinning centers is similar to the coherence length of normal MgB 2 (about 12 nm) [31], which results in the improvement of superconducting properties. Most oxidative metamorphic MgB 2 grains and MgO secondary particles are too large to be effective pinning centers, which are harmful to the connectivity between normal MgB 2 grains and have a negative effect on J C , as shown in Figure 4, with the decrease of J C in the PaF of both samples. There are more grain boundaries in the PeF of both samples, which are prone to GBP to improve the superconducting properties of MgB 2 bulks [28,29], which is consistent with the higher J C of the PeF in both samples, as shown in Figures 4 and 5. Moreover, the existence of more small-sized particles in the PeF of the S1 sample may be related to the highest self-field J C , as shown in Figure 4.  Figure 6 shows a SEM diagram of the PaF (left) and PeF (right) of the SPSed samples. It is found that some large and white round and oval particles appear in the PaF of both samples, which are oxidative metamorphic MgB2 grains or MgO secondary particles [7,8]. It has been shown that the size of the effective pinning centers is similar to the coherence length of normal MgB2 (about 12 nm) [31], which results in the improvement of superconducting properties. Most oxidative metamorphic MgB2 grains and MgO secondary particles are too large to be effective pinning centers, which are harmful to the connectivity between normal MgB2 grains and have a negative effect on JC, as shown in Figure 4, with the decrease of JC in the PaF of both samples. There are more grain boundaries in the PeF of both samples, which are prone to GBP to improve the superconducting properties of MgB2 bulks [28,29], which is consistent with the higher JC of the PeF in both samples, as shown in Figures 4 and 5. Moreover, the existence of more small-sized particles in the PeF of the S1 sample may be related to the highest self-field JC, as shown in Figure 4.   Table 1. The horizontal axis is the range of the crystallite size, and the vertical axis is the percentage of the number of MgB2 grains in a certain size range based on the total statistical MgB2 grains in each specimen. It is easy to see that S1-PeF has the smallest av-   Table 1. The horizontal axis is the range of the crystallite size, and the vertical axis is the percentage of the number of MgB 2 grains in a certain size range based on the total statistical MgB 2 grains in each specimen. It is easy to see that S1-PeF has the smallest average size (0.24 µm), and S2-PaF has the largest average size (0.29 µm). A smaller crystal size means more MgB 2 particles and grain boundaries per unit volume, which can increase the number of effective pinning centers and further improve the J C of MgB 2 [32]. This is consistent with the trend of J C in Figures 3 and 4, which confirms that the J C is greatly influenced by the crystal size of the SPSed MgB 2 bulks. erage size (0.24 µm), and S2-PaF has the largest average size (0.29 µm). A s size means more MgB2 particles and grain boundaries per unit volume, crease the number of effective pinning centers and further improve the JC This is consistent with the trend of JC in Figures 3 and 4, which confirms greatly influenced by the crystal size of the SPSed MgB2 bulks.

The Flux-Pinning Mechanism
To study the flux-pinning mechanism, two scaling procedures shou identify the dominant pinning mechanism from the peak position [33,34]. Dew-Hughes [33], one of them is the universal law Fp = Ah p (1 − h) q (where and Fp is the volume pinning force. Another equation is Fp = μ0H × JC and field; it can be presented by the equation h = H/Hirr). The law was chosen to Fp and H/Hirr. The parameter h0 is the field when Fp reaches its maximum, nents p and q are fitted from the data of Fp and H/Hirr, which analyzes the behavior more deeply and easily. Figure 8 shows the curves of the parame the pinning force: h0 (a), p (b), and q (c) as a function of the preparation tem h0 (a1), p (b1), and q (c1) as a function of test temperature. The theoretical GBP and PP for reference are represented by the dotted lines. For isotro GBP is identified by h0 = 0.2, p = 0.5, and q = 2, while PP is identified by h and q = 2. However, this scaling procedure has its limitation for MgB2 mate it does not apply to untextured, anisotropic materials. Therefore, another dure, whose parameter Kn is presented by Kn = h0/hn (where hn refers to the is halved), was proposed by Eisterer [34], to analyze the flux-pinning m achieve a more accurate flux-pinning mechanism behavior. As a modifie cedure, it can greatly reduce the influence of previously unknown parame ropy. The Kn values of 0.34 and 0.47 are defined for GBP and PP, respect plots of Kn (d) and (d1) as functions of the preparation temperature and the ture are shown in Figure 8. These two procedures mentioned above will b discuss the pinning mechanism of the samples.

The Flux-Pinning Mechanism
To study the flux-pinning mechanism, two scaling procedures should be used to identify the dominant pinning mechanism from the peak position [33,34]. According to Dew-Hughes [33], one of them is the universal law F p = Ah p (1 − h) q (where A is constant, and F p is the volume pinning force. Another equation is F p = µ 0 H × J C and h is a reduced field; it can be presented by the equation h = H/H irr ). The law was chosen to fit the data of F p and H/H irr . The parameter h 0 is the field when F p reaches its maximum, and the exponents p and q are fitted from the data of F p and H/H irr , which analyzes the flux-pinning behavior more deeply and easily. Figure 8 shows the curves of the parameters related to the pinning force: h 0 (a), p (b), and q (c) as a function of the preparation temperature and h 0 (a 1 ), p (b 1 ), and q (c 1 ) as a function of test temperature. The theoretical values of the GBP and PP for reference are represented by the dotted lines. For isotropic materials, GBP is identified by h 0 = 0.2, p = 0.5, and q = 2, while PP is identified by h 0 = 0.33, p = 1, and q = 2. However, this scaling procedure has its limitation for MgB 2 materials, because it does not apply to untextured, anisotropic materials. Therefore, another scaling procedure, whose parameter K n is presented by K n = h 0 /h n (where h n refers to the field when F p is halved), was proposed by Eisterer [34], to analyze the flux-pinning mechanism to achieve a more accurate flux-pinning mechanism behavior. As a modified scaling procedure, it can greatly reduce the influence of previously unknown parameters of anisotropy. The K n values of 0.34 and 0.47 are defined for GBP and PP, respectively, and the plots of K n (d) and (d 1 ) as functions of the preparation temperature and the test temperature are shown in Figure 8. These two procedures mentioned above will be combined to discuss the pinning mechanism of the samples. It is obvious from Figure 8a,d that the values of the pinning force related to param eters h0 and Kn of the PeF are lower than those of the PaF, except for Kn of the PeF of S1 which means that the PeF has a stronger GBP than the PaF. Based on the previous repor It is obvious from Figure 8a,d that the values of the pinning force related to parameters h 0 and K n of the PeF are lower than those of the PaF, except for K n of the PeF of S1, which means that the PeF has a stronger GBP than the PaF. Based on the previous report [7,35], the smaller crystallite size causes more grain boundaries per unit volume, which means a stronger GBP, as shown in the microstructure of Figure 6 and the smaller crystallite size of Figure 7, accompanied by a better superconducting performance of the PeF in both samples. The values of the pinning force-related parameters h 0 and K n of the PeF of S2 decrease with the increase in the preparation temperature of the MgB 2 bulk samples, which means that S2 has a stronger GBP than S1. We can speculate that the crystallite size of S2 is smaller than the crystallite size of S1. In addition, according to this deduction, J C of S2 should be higher than that of S1 in a magnetic field, but the trend of J C is opposite to this rule, as shown in Figures 4 and 5. This represents that GBP is not the only factor affecting J C in the PeF of S1. There must be other factors that influence it-maybe the secondary phase particles in the suitable size, such as MgO or MgB 4 , etc. The right picture shows the chemical composition of the area circled in red in the left picture, as shown in Figure 9. From the EDS spectra, we can calculate the chemical formula and then verify the existence of MgO particles, which is confirmed by the XRD analysis of Figure 2. MgO particles can be effective pinning centers. In addition, both PP and GBP work on J C at the same time to result in the improvement of J C in the PeF of the S1 sample under the lower preparation temperature, as shown in Figures 4 and 5. The discrepancy of S2 under higher preparation temperature in the parameters h 0 and K n is higher than that of S1, which is related to the increasing anisotropy of the SPSed samples, which accounts for the difference in properties between the PeF and PaF of S2. This is not conducive to practical application. , 14, 988 9 of 12 tallite size of Figure 7, accompanied by a better superconducting performance of the PeF in both samples. The values of the pinning force-related parameters h0 and Kn of the PeF of S2 decrease with the increase in the preparation temperature of the MgB2 bulk samples, which means that S2 has a stronger GBP than S1. We can speculate that the crystallite size of S2 is smaller than the crystallite size of S1. In addition, according to this deduction, JC of S2 should be higher than that of S1 in a magnetic field, but the trend of JC is opposite to this rule, as shown in Figures 4 and 5. This represents that GBP is not the only factor affecting JC in the PeF of S1. There must be other factors that influence it-maybe the secondary phase particles in the suitable size, such as MgO or MgB4, etc. The right picture shows the chemical composition of the area circled in red in the left picture, as shown in Figure 9. From the EDS spectra, we can calculate the chemical formula and then verify the existence of MgO particles, which is confirmed by the XRD analysis of Figure 2. MgO particles can be effective pinning centers. In addition, both PP and GBP work on JC at the same time to result in the improvement of JC in the PeF of the S1 sample under the lower preparation temperature, as shown in Figures 4 and 5. The discrepancy of S2 under higher preparation temperature in the parameters h0 and Kn is higher than that of S1, which is related to the increasing anisotropy of the SPSed samples, which accounts for the difference in properties between the PeF and PaF of S2. This is not conducive to practical application. The relationship between the pinning mechanism and the critical current of MgB2 bulks has been studied, and further investigation of the relationship between pinning force-related parameters and JC in high magnetic fields has been studied as well. It is inferred that more grain boundaries can enhance the Hc2 [33,36], which can be presented by Hirr [30,36], so we can predict that stronger GBP can lead to higher Hirr and then improve JC in high magnetic fields [7]. This coincides with the result, as shown in Figures 4  and 5, which has the best performance in a high magnetic field in JC of S2-PeF.
It is evident that the values of h0 and Kn in the PeF of both samples, as shown in Figure 8a 1 , become larger with the increase in the test temperature, from 10 K to 30 K, which means the PP grows stronger. The stronger PP indicates that much more effective pinning centers exist, and these effective pinning centers can bring higher JC. This is consistent with our observation of the MgO second phases in Figure 2, which can be effec- The relationship between the pinning mechanism and the critical current of MgB 2 bulks has been studied, and further investigation of the relationship between pinning force-related parameters and J C in high magnetic fields has been studied as well. It is inferred that more grain boundaries can enhance the H c2 [33,36], which can be presented by H irr [30,36], so we can predict that stronger GBP can lead to higher H irr and then improve J C in high magnetic fields [7]. This coincides with the result, as shown in Figures 4 and 5, which has the best performance in a high magnetic field in J C of S2-PeF.
It is evident that the values of h 0 and K n in the PeF of both samples, as shown in Figure 8a 1 , become larger with the increase in the test temperature, from 10 K to 30 K, which means the PP grows stronger. The stronger PP indicates that much more effective pinning centers exist, and these effective pinning centers can bring higher J C . This is consistent with our observation of the MgO second phases in Figure 2, which can be effective pinning centers. This theory is consistent with the performance of J C , as shown in Figure 5. We can notice that the values of h 0 and K n of the PaF in both samples from Figure 8a 1 ,d 1 are not a monotonous trend, but rather a fluctuation, which is not consistent with the conclusion that PP as the main pinning becomes stronger as the test temperature increases, which means that the values of h 0 and K n show an overall increasing trend with increasing test temperature [19,36,37]. Maybe some evidence can be found from some studies with small temperature intervals [21,37]. The change in anisotropy or percolation with temperature may cause this temperature dependence of the pinning mechanism [7].

Conclusions
In this study, we prepared two MgB 2 bulk samples, with a disc shape of 20 mm in diameter and 3 mm in thickness, at different temperatures of 950 • C (marked S1) and 975 • C (marked S2) for 2 h under 50 MPa pressure using the spark plasma sintering technique. The properties of the samples were analyzed according to the results of magnetization measurement and SEM diagrams. Critical temperature (T C ), critical current density (J C ), microstructure, and the pinning mechanism of the perpendicular facets (PeF) and parallel facets (PaF) to the compression direction of MgB 2 bulk samples are all included. The onset of critical temperature is around 37.5 K and the transition width is about 1 K, which indicates all samples exhibit good crystallinity and homogeneity. In terms of T C , the onset transition temperature, T c,onset , of S1 is slightly higher than that of the S2 sample, which may be related to the good performance of the S1 sample. In terms of J C , the critical current density of all MgB 2 bulk samples decreases with the increase of the applied field. In a low magnetic field, S1-PeF has the highest J C (342 kA/cm 2 ), followed by S2-PeF (333 kA/cm 2 ), S1-PaF (326 kA/cm 2 ), and S2-PaF (317 kA/cm 2 ) in self-field at 20 K, respectively. The crystal size of the samples is 0.24 µm (S1-PeF), 0.25 µm (S2-PeF), 0.27 µm (S1-PaF), and 0.29 µm (S2-PaF), respectively. Thus, the values of J C and the crystal size of samples obey the rule that a smaller crystal size can improve the J C of MgB 2 samples. However, in a high magnetic field, the S2-PeF has the highest J C , which contradicts the rule above. It illustrates that other factors can affect J C . According to the pinning mechanism, we find the factor is GBP, where stronger GBP can improve the J C in a high magnetic field. In terms of the pinning mechanism, according to the analysis of the trend of the parameters h 0 , p, q, and K n , the PeF has a stronger GBP than the PaF, which is related to the smaller crystallite size, resulting in more grain boundaries per unit volume. Therefore, PeF shows better superconducting performance with an increase in the preparation temperature. The existence of a slightly higher discrepancy of properties occurs in the S2 sample. In addition, with the increase in temperatures, PP grows stronger, bringing higher J C . It is clear that the PeF and PaF of S1 processed under a lower prepared temperature possess the optimum superconducting performance in a low magnetic field; however, J C of the PeF of the S2 sample processed under a higher prepared temperature is more advantageous in a high magnetic field. Therefore, further suitable preparation temperatures to fabricate MgB 2 superconductor bulks using the SPS technique will appear in future experiments.