**High Critical Current Density MgB2**

Wenxian Li and Shi-Xue Dou

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/59492

#### **1. Introduction**

[32] Mitchell E. E. and Foley C. P. YBCO step-edge junctions with high IcRn. Supercond.

[33] Clarke J., "SQUID Fundamentals", in: H. Weinstock (Ed.), SQUID Sensors: Funda‐ mentals, Fabrication and Applications (NATO ASI Series E: Applied. Science. 329),

[34] Schmelz M., Stolz R., Zakosarenko V., Anders S., Fritzsch L., Roth H., Meyer H.-G. Highly sensitive miniature SQUID magnetometer fabricated with cross-type Joseph‐

[35] Faley M. I., Poppe U., Urban K., Paulson D. N., Starr T., and Fagaly R. L. Low noise HTS dc-SQUID flip-chip magnetometers and gradiometers. IEEE Transactions on

[36] Matlashov A., Bakharev A., Zhuravlev Y., and Slobodchikov V. Biomagnetic multichannel system consisting of several self-contained autonomous small-size units. In: Koch H. and Lübbig H. (ed.) Superconducting Devices and Their Applications. Ber‐

[37] Fagaly R. L. Neuromagnetic instrumentation. In: Sato S. (ed.) Advances in Neurolo‐

[38] Malmivuo J. Comparison of the Properties of EEG and MEG in Detecting the Electric

gy. New York: Raven Press; 1990;54: Magnetoencephalography 11-32.

Activity of the Brain. Brain Topography. 2012;25 1–19.

Sci. Technol. 2010;23 065007.

94 Superconductors – New Developments

Kluwer Academic, Dordrecht, 1996 p.1–62.

Appl. Supercond. 2001;11(1) 1383-1386.

lin: Springer-Verlag; 1992;64 511-516.

son tunnel junctions. Physica C. 2012;478 77–80.

The highest critical transition temperature (*Tc*) among all the intermetallic superconductors in that was discovered MgB2 has changed the previous approaches to the theory of supercon‐ ductivity because the *Tc* limit in metallic superconductors had been believed to be ~ 30 K, which is predicted by the Bardeen-Cooper-Schrieffer (BCS) theory [1]. In the BCS theory of super‐ conductivity [2, 3], the expression for *Tc* is derived as *Tc* =*θ*e (−1/*λ*eff) , where *θ* is always equal to the MgB2 Debye temperature, *θD*. *λ*eff is defined as the electron and phonon coupling constant *λ* = *N*(*E*F)× *V*. *N*(*E*F) is the normal state electron number density the Fermi surface, and *V* is the average electron interaction matrix element corresponding to the attraction. A weak coupling, *λ* << 1, is assumed to exist between the electrons and phonons in the initial BCS theory. In this case, the value of *Tc* is limited to *Tc* ≈ 30 K. According to the BCS theory, an element or compound with larger *N(E*F*)*, *V*, and *θ*D has high *Tc* value. However, *θ*D of MgB2 is comparable to those of other diborides and other light materials. Furthermore, the *N(E*F*)* is relatively low because of the absence of *d*-electrons. Thus, the unusually high *Tc* in MgB2 has confused researchers with respect to the origin of its superconductivity. Considerable theoretical and experimental work has been conducted to explore the superconducting mechanism in MgB2.

MgB2 is the first superconductor to be proved to have two distinct superconducting gaps in its superconducting state [4]. Initially, an unconventional exotic superconducting mechanism was suggested for the material [5, 6]. Then, other researchers proposed hole superconductivity, which is similar to what occurs in high temperature superconductors (HTS), based on the fact that holes are the dominant charge carriers in the normal state [7, 8]. MgB2 has now been accepted as a phonon-mediated BCS type superconductor. The superconductivity is attributed to selective coupling between specific electronic states and specific phonons, such as the *E*2*<sup>g</sup>* mode. The unusually high *Tc* value arises from the strong phonon anharmonicity.

© 2015 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Choi*et al.*havecalculatedthephononfrequenciesandelectron-phononinteractions fromfrozen phonon calculations at allthe symmetrypoints oftheBrillouin zone [9]. Six non-acoustic modes at the Brillouin zone centre Γ are divided into four distinct phonon modes based on the point symmetry of the lattice. The two vibrations along the *c-*axis are singly degenerate modes of *A*2*<sup>u</sup>* and *B*1*<sup>g</sup>*. For the *A*2*<sup>u</sup>* mode, both Mg and B move in opposite directions along *c*. For *B*1*<sup>g</sup>*, the B atoms move in opposite directions, while the Mg is stationary. The other two modes along the *x* or *y* directions involving only in-plane motions are doubly degenerate. The vibration of Mg andBplanesinoppositedirectionsalongthe*x*or*y*directionsis*E*1*<sup>u</sup>*mode.Mgatomsarestationary in the *E*2*<sup>g</sup>* mode, while B atoms exhibit a breathing vibration in the *x* or *y* directions. This mode is highly anharmonic. The theoretical vibration energy of the *E*2*<sup>g</sup>* mode is around 75 meV [10, 11], which is in agreement with the results from Raman measurements [12, 13].

MgB<sup>2</sup> is easy to make into bulk, wire, tape, and thin film forms. However, the critical current density (*Jc*) of pristine MgB2 drops rapidly in high magnetic field due to the weak pinning forces and low upper critical field (*Hc*2). Many techniques have been employed to improve the application potential of MgB2, such as chemical doping, irradiation, thermo-mechanical processing, and magnetic shielding. Although the critical current density, upper critical field, and irreversibility field (*Hirr*) have been greatly increased [14], many difficulties need to be overcome for further application. The origin of the flux pinning force and relevant fabrication techniques will be discussed in this work. Lattice distortion is found to be one of the most effective sources of flux pinning centers in pure MgB2. Then, the combined effects of connec‐ tivity and lattice disorder on the flux pinning force are investigated based on nanosize SiC doped MgB2.

The depairing current density, *Jd*, can be estimated from the Ginzburg-Landau (GL) formula:

$$J\_d = \Phi\_0 \land \left[ \Im \left( \sqrt{\mathfrak{J}} \right) \pi \mu\_0 \mathcal{k}^2(T) \xi(T) \right],\tag{1}$$

where *Φ*0 is the flux quantum, *μ*0 the permeability of vacuum, *λ* the penetration depth, and *ξ* the coherence length [15]. However, it is not the theoretical maximum [16]. With the help of optimized pinning, about 15% of *Jd* can be obtained at low magnetic fields in superconductors [17, 18]. The high field values for pure MgB2 are *λ* = 80 nm and *ξ* = 12 nm, respectively. *Jd* at zero K is estimated as ~1*.*3 × 10<sup>8</sup> A.cm−2. The contribution from *π*-band charge carriers to the depairing current density is quite low, only about 10% [16], and the interaction energy induces the difference from the high field value. The depairing current is reduced in samples with defects because of the increased *λ* values [18].

The grain boundaries in MgB2 do not show the weak link effect, and clean grain boundaries are not obstacle to supercurrents [19, 20]. On the other hand, dirty grain boundaries do potentially reduce the critical current [21]. Insulating phases on the grain boundaries, such as MgO, boron oxides [22] or boron carbide [23], normal conducting phases [24], porosity, and cracks [25], can further reduce the cross-section effective of supercurrents. The high porosity in *in-situ* prepared MgB2 is responsible for its low density, only about half (or less) of its theoretical value [26].

The concept of connectivity, *A*con, has been introduced to quantify the effective cross-section (*σ*eff) for supercurrents [21, 27]: *A*con = *σ*eff / *σ*0, where *σ*0 is the geometrical cross-section. The connectivity is estimated from the phonon contribution to the normal state resistivity through *A*con ≈ *Δρ*theo/*Δρ*exp, with *Δρ*theo ≈ 9 *μ*Ω cm. This estimate is based on the assumption that *σ*eff is reduced equivalently in the normal and superconducting state [18]. The supercurrents are limited by the smallest effective cross-section along the conductor. A single large transverse crack can reduce strongly *J*c, while only slightly increases the resistivity of a long sample. Unreacted magnesium decreases *Δρ*exp [28] and the effective paths for supercurrents. The thin insulating layers located on grain boundaries can decrease the effective connectivity *A*con, inducing high *Δρ*exp, although this kind of defect is transparent to supercurrents. The *Δρ*theo values within the grains depend on the defects and strain in the grains. Sharma observed negative *Δρ*exp in highly resistive samples [29]. Despite these objections, *A*con is very useful for estimating the connectivity of samples if the resistivity is not too high. A clear correlation between the resistivity and the critical current was found in thin films [27]. It should be noted that this procedure is not always reliable, although it offers a possibility for understanding the influences of the connectivity on the supercurrent [18].

Choi*et al.*havecalculatedthephononfrequenciesandelectron-phononinteractions fromfrozen phonon calculations at allthe symmetrypoints oftheBrillouin zone [9]. Six non-acoustic modes at the Brillouin zone centre Γ are divided into four distinct phonon modes based on the point symmetry of the lattice. The two vibrations along the *c-*axis are singly degenerate modes of *A*2*<sup>u</sup>* and *B*1*<sup>g</sup>*. For the *A*2*<sup>u</sup>* mode, both Mg and B move in opposite directions along *c*. For *B*1*<sup>g</sup>*, the B atoms move in opposite directions, while the Mg is stationary. The other two modes along the *x* or *y* directions involving only in-plane motions are doubly degenerate. The vibration of Mg andBplanesinoppositedirectionsalongthe*x*or*y*directionsis*E*1*<sup>u</sup>*mode.Mgatomsarestationary in the *E*2*<sup>g</sup>* mode, while B atoms exhibit a breathing vibration in the *x* or *y* directions. This mode is highly anharmonic. The theoretical vibration energy of the *E*2*<sup>g</sup>* mode is around 75 meV [10,

MgB<sup>2</sup> is easy to make into bulk, wire, tape, and thin film forms. However, the critical current density (*Jc*) of pristine MgB2 drops rapidly in high magnetic field due to the weak pinning forces and low upper critical field (*Hc*2). Many techniques have been employed to improve the application potential of MgB2, such as chemical doping, irradiation, thermo-mechanical processing, and magnetic shielding. Although the critical current density, upper critical field, and irreversibility field (*Hirr*) have been greatly increased [14], many difficulties need to be overcome for further application. The origin of the flux pinning force and relevant fabrication techniques will be discussed in this work. Lattice distortion is found to be one of the most effective sources of flux pinning centers in pure MgB2. Then, the combined effects of connec‐ tivity and lattice disorder on the flux pinning force are investigated based on nanosize SiC

The depairing current density, *Jd*, can be estimated from the Ginzburg-Landau (GL) formula:

where *Φ*0 is the flux quantum, *μ*0 the permeability of vacuum, *λ* the penetration depth, and *ξ* the coherence length [15]. However, it is not the theoretical maximum [16]. With the help of optimized pinning, about 15% of *Jd* can be obtained at low magnetic fields in superconductors [17, 18]. The high field values for pure MgB2 are *λ* = 80 nm and *ξ* = 12 nm, respectively. *Jd* at

depairing current density is quite low, only about 10% [16], and the interaction energy induces the difference from the high field value. The depairing current is reduced in samples with

The grain boundaries in MgB2 do not show the weak link effect, and clean grain boundaries are not obstacle to supercurrents [19, 20]. On the other hand, dirty grain boundaries do potentially reduce the critical current [21]. Insulating phases on the grain boundaries, such as MgO, boron oxides [22] or boron carbide [23], normal conducting phases [24], porosity, and cracks [25], can further reduce the cross-section effective of supercurrents. The high porosity in *in-situ* prepared MgB2 is responsible for its low density, only about half (or less) of its

( ) ( ) ( ) <sup>2</sup> 0 0 / 3/ 3 , = F é ù ë û *<sup>d</sup> <sup>J</sup>* pm l

 x

*T T* (1)

A.cm−2. The contribution from *π*-band charge carriers to the

11], which is in agreement with the results from Raman measurements [12, 13].

doped MgB2.

96 Superconductors – New Developments

zero K is estimated as ~1*.*3 × 10<sup>8</sup>

theoretical value [26].

defects because of the increased *λ* values [18].

The *in-situ* route is a practical technique to improve the *Hc*2 and *Jc* performance of MgB2 using magnesium or MgH2 as the precursor material [30-39], which reacts with boron after mixing and compacting. Low annealing temperature generates MgB2 samples with small grains [25, 40-52] due to the poor crystallinity, and the great amount of grain boundaries result in strong pinning and high *H*c2. Magnesium deficient samples can be fabricated by adjusting the stoichiometry of the precursor materials. This method can generate strong lattice strain in MgB2, which decreases *T*c, and increases *H*c2 [44, 53-56]. On the other hand, an excess magne‐ sium ratio in the raw materials can compensate for the evaporation loss of Mg due to its low melting temperature and the reaction loss due to the reaction with oxygen or the sheath material. The morphology and particle size of the precursor magnesium powders are crucial for the superconductivity and superconducting performance of the final MgB2 [57]. The grain size of the initial boron powder also has a significant influence on the MgB2 samples. Some researchers have employed ball milling and mechanical alloying of the magnesium and boron mixture, reducing the grain size and enhancing the critical supercurrent [55, 58-65].

The reaction kinetics between magnesium and boron can be modified by chemical or com‐ pound dopants [66], which influence the grain shape and size [67, 68], the secondary phases [69], MgB2 density [70], and the element stoichiometry [71]. Carbon doping is one of the most promising methods to improve the superconducting performance of MgB2. The carbon sources include B4C [72, 73], carbon [52, 66, 67, 74], carbon nanotubes [75-78], nanodiamonds [78, 79], NbC [80], SiC [41, 51, 57, 66, 72, 81-89], and organic compounds [39, 47, 90]. SiC is one of the most promising dopants because it can react with magnesium and boron to form C doped MgB2 at quite low temperatures (600 o C), based on the dual reaction model [66]. Higher processing temperatures are necessary for most of the other carbon sources, leading to grain growth and worse pinning. Comparable results to those with SiC have also obtained, however, with nanoscale carbon powder [91], stearic acid [92], and carbon nanotubes [76].

The *in-situ* technique also suffers from its disadvantage of low mass density, which is originates from the annealing process, because the precursor powder has a lower density than MgB2. High pressure synthesis increases the density [93, 94]. On the other hand, the density of *exsitu* materials is usually close to the real density of MgB2 [94] and can be further improved by hot isostatic pressing (HIP) [91, 95, 96]. However, the grain size of *ex-situ* produced materials is comparatively large and inhomogeneous due to the post annealing [97, 98]. Small grains (~ 100–200 nm) have also been reported [99]. A high temperature heat treatment is necessary for the *ex-situ* process to improve the connectivity [99-102]. This heat treatment leads to recrys‐ tallization and *H*c2 reduction [25]. It is concluded that disorder induced by the low temperature processing is insufficient for high superconducting performance of the *ex-situ* MgB2. Further‐ more, thermally stable defects, such as dopants, are necessary for enhancing the high field performance [18].

## **2. Thermal-strain-induced high** *Jc* **in high density SiC-MgB2 bulk**

The connectivity is considered to be a critical issue for improving the *Jc* of MgB2 based superconductors. Furthermore, an efficient flux pinning force is crucial for high magnetic field application. Here, we employed an *in-situ* diffusion process to make high density MgB2 bulks and investigate the efficiency of the high flux pinning force induced by lattice thermal strain [103]. Microstructural analysis and Raman scattering measurements were employed to investigate the origins of the huge flux pinning force. Doping nano-SiC particles into MgB2 has been proven to be particularly effective in significantly enhancing *Jc*, *Hirr*, and *Hc*<sup>2</sup> [14, 104, 105]. In contrast to chemical doping effects, tensile stress is believed to act as a source of strong flux pinning centers when there is no reaction between SiC and MgB2. Both the *Jc* and *Tc* are improved by thermal strain on the interface between SiC and MgB2 during the diffusion process [106] and hybrid physical-chemical vapor deposition (HPCVD) [107]. The influences of the stress field on the flux pinning force and the electron-phonon coupling constant are discussed to clarify the superconducting performance of high density SiC-MgB2 composite fabricated through the diffusion method.

Crystalline B with 99.999% purity was pressed into pellets or mixed with 10wt% SiC particles and then pressed into pellets. The pellets were sealed in iron tubes and padded with 99.8% Mg powder. The Mg to B atomic ratio was 1.15:2.0. The diffusion process is time dependente. The sintering condition were 1123 K for 10 h under a flow of high purity argon gas to achieve fully reacted MgB2 bulks. Then the samples were cooled down to room temperature. X-ray diffrac‐ tion (XRD) was employed to characterize the phases, and the results were refined to deter‐ mine the *a*-axis and *c*-axis lattice parameters and the lattice distortion. Microstructure observations were performed with a transmission electron microscope (TEM). The magnetic *Jc* was derived from the height of the magnetization loop Δ*M* using the Bean model: *Jc* = 15Δ*M*/[*π a*3 *h*)], where *a* and *h* are the radius and height of a cylindrical sample. The *Tc* value could be deduced from the temperature dependence curve of the magnetic susceptibility *M*(*T*). To observe the temperature effects of lattice strain, Raman spectra were collected using a confo‐ cal laser Raman spectrometer (Renishaw inVia plus) under a 100× microscope. The excitation laser is Ar+ 514.5 nm.

The density of the pure MgB2 sample is about 1.86 g/cm3 , which is about 80% of the theoretical density. This value is much higher than those of the samples made by the *insitu* process, which were less than 50%. The SiC-MgB2 composite shows an even higher density of 1.91 g/cm3 due to the SiC addition. Figure 1 shows the Rietveld refinement XRD patterns of the pure MgB2 and the 10wt% SiC doped MgB2 samples. In this case, SiC did not react with magnesium and boron to form C doped MgB2 and Mg2Si. The product is a SiC-MgB2 composite. The Rietveld refinement analysis indicates that the unreacted SiC content was about 9.3wt%, similar to the SiC content in the precursor. This is consistent with the absence of Mg2Si in the XRD pattern as shown in Figure 1. The result is differ‐ ent when the SiC-doped MgB2 prepared by the *in-situ* technique [14, 41, 84], in which only a very small amount of SiC remaines, while Mg2Si is always present due to the reaction of Mg with SiC. The *a-* and *c*-axis lattice parameters were 3.0850 Å and 3.5230 Å for pure MgB2, and 3.0840 Å and 3.5282 Å for SiC doped MgB2, respectively. The *a*-axis parame‐ ters are virtually equivalent for the two samples, whereas the *c*-axis one is slightly stretched in the SiC-MgB2 composite. The phenomenon is different from the shortening of the *a*axis parameter in *in-situ* processed SiC doped MgB2, while the *c*-axis parameter remains unchanged [14, 89].

The *in-situ* technique also suffers from its disadvantage of low mass density, which is originates from the annealing process, because the precursor powder has a lower density than MgB2. High pressure synthesis increases the density [93, 94]. On the other hand, the density of *exsitu* materials is usually close to the real density of MgB2 [94] and can be further improved by hot isostatic pressing (HIP) [91, 95, 96]. However, the grain size of *ex-situ* produced materials is comparatively large and inhomogeneous due to the post annealing [97, 98]. Small grains (~ 100–200 nm) have also been reported [99]. A high temperature heat treatment is necessary for the *ex-situ* process to improve the connectivity [99-102]. This heat treatment leads to recrys‐ tallization and *H*c2 reduction [25]. It is concluded that disorder induced by the low temperature processing is insufficient for high superconducting performance of the *ex-situ* MgB2. Further‐ more, thermally stable defects, such as dopants, are necessary for enhancing the high field

**2. Thermal-strain-induced high** *Jc* **in high density SiC-MgB2 bulk**

The connectivity is considered to be a critical issue for improving the *Jc* of MgB2 based superconductors. Furthermore, an efficient flux pinning force is crucial for high magnetic field application. Here, we employed an *in-situ* diffusion process to make high density MgB2 bulks and investigate the efficiency of the high flux pinning force induced by lattice thermal strain [103]. Microstructural analysis and Raman scattering measurements were employed to investigate the origins of the huge flux pinning force. Doping nano-SiC particles into MgB2 has been proven to be particularly effective in significantly enhancing *Jc*, *Hirr*, and *Hc*<sup>2</sup> [14, 104, 105]. In contrast to chemical doping effects, tensile stress is believed to act as a source of strong flux pinning centers when there is no reaction between SiC and MgB2. Both the *Jc* and *Tc* are improved by thermal strain on the interface between SiC and MgB2 during the diffusion process [106] and hybrid physical-chemical vapor deposition (HPCVD) [107]. The influences of the stress field on the flux pinning force and the electron-phonon coupling constant are discussed to clarify the superconducting performance of high density SiC-MgB2 composite

Crystalline B with 99.999% purity was pressed into pellets or mixed with 10wt% SiC particles and then pressed into pellets. The pellets were sealed in iron tubes and padded with 99.8% Mg powder. The Mg to B atomic ratio was 1.15:2.0. The diffusion process is time dependente. The sintering condition were 1123 K for 10 h under a flow of high purity argon gas to achieve fully reacted MgB2 bulks. Then the samples were cooled down to room temperature. X-ray diffrac‐ tion (XRD) was employed to characterize the phases, and the results were refined to deter‐ mine the *a*-axis and *c*-axis lattice parameters and the lattice distortion. Microstructure observations were performed with a transmission electron microscope (TEM). The magnetic *Jc* was derived from the height of the magnetization loop Δ*M* using the Bean model: *Jc* = 15Δ*M*/[*π*

*h*)], where *a* and *h* are the radius and height of a cylindrical sample. The *Tc* value could be deduced from the temperature dependence curve of the magnetic susceptibility *M*(*T*). To observe the temperature effects of lattice strain, Raman spectra were collected using a confo‐ cal laser Raman spectrometer (Renishaw inVia plus) under a 100× microscope. The excitation

performance [18].

98 Superconductors – New Developments

*a*3

laser is Ar+

514.5 nm.

fabricated through the diffusion method.

**Figure 1.** Rietveld refined XRD patterns of pure MgB2 and 10wt% SiC doped MgB2 samples made by the diffusion process at 850 o C for 10 h. The *a*-axis parameters are virtually the same for the two samples, whereas the *c*-axis parame‐ tar is stretched in the SiC-MgB2 composite.

To explain the abnormal *c*-axis enlargement of the SiC-MgB2 composite, the thermal expansion coefficients, *α*, of MgB2 and SiC are considered. It is reasonable to assume that both the MgB2 and the SiC are in a stress-free state at the sintering temperature of 1123 K due to the relatively high sintering temperature over a long period of time. However, the lattice parameters are determined by the thermal strain during the cooling process. The temperature dependences of the *α* values for MgB2 and SiC are especially different. Figure 2(a) plots the *α*(*T*) for MgB2 and SiC along the *a*- and *c*-axes, based on the data of References [108-111]. It clearly shows the weak temperature dependence of*α*(*T*) for SiC in both directions, whereas the changes are great for MgB2 and are characterized by high anisotropy. The averaged *α*(*T*) is also huge in MgB2 as

**Figure 2.** (a) Thermal expansion coefficients (*α*) along the a-axis and c-axis for MgB2 and SiC as a function of tempera‐ ture. The averaged *α*(T) values for MgB2 and SiC are plotted in the inset. (b) Plots of the normalized lattice changes for MgB2 and SiC, and the thermal strain in the matrix during cooling from 1123 K to 0 K.

shown in the inset of Figure 2(a). The *α*SiC decreases slightly from 5×10-6/K at 1123 K to 2.5×10-6/ K at 0 K, whereas the *α*MgB2 drops quickly from 1.7×10-5/K at 1123 K to zero at 0 K. Based on

*α*(*T*), the normalized lattice change and lattice strain in the MgB2 matrix of SiC-MgB2 composite during cooling from 1123 K to 0 K can be derived, as shown in Figure 2(b). An assumption of Figure 2(b) is that the two phases are strongly connected and the volume shrinkage of MgB2 is confined by the relatively stable SiC. The normalized lattice strain is estimated to be -0.55% in SiC-MgB2 along the *c-*axis at room temperature. The negative value corresponds to tensile strain in the MgB2. The large *c*-axis strain in the doped MgB2 results in an enlargement in the *c*-axis by 0.15 % in comparison with pure MgB2. As estimated from the Williamson-Hall model [112], the lattice strain is 0.208 and 0.306 along the *a-*axis, and 0.292 and 1.13 along the *c-*axis for pure and SiC-MgB2, respectively. The lattice strain along the *c-*axis in the SiC-MgB2 has increased from that of pure MgB2 by a factor of 4, which is attributed to the high anisotropy in the thermal expansion coefficient of MgB2.

**Figure 3.** (a) Bright field TEM image of the pure MgB2 with indexed SAD pattern (inset). (b) High resolution electron mi‐ croscope (HREM) image of interface in pure MgB2 with FFT pattern along the [100] axis (inset). (c) Bright field TEM im‐ age of SiC-MgB2. (d) HREM image of interface in SiC-MgB2 and FFT patterns of SiC and MgB2 from each side of the interface. The dashed line shows the interface of SiC and MgB2.

The unreacted SiC buried in the MgB2 matrix is believed to be one of the most effective sources of strain, and the strongly connected interfaces of SiC and MgB2 are the most effective flux pinning centers. The micro morphologies can be detected using TEM to explore the defects and grain boundaries both in the pure MgB2 and in the SiC-MgB2. Figures 3(a) shows a bright field image of pure MgB2. A high density of defects, such as dislocations and lattice distortion, is observed in the MgB2 phase, and the grain size is about 100 nm,as estimated from the grain boundaries. In contrast to with the highly porous structure in the MgB2 samples [91], the samples made by the diffusion process are well connected with high density. The indexed selected area diffraction (SAD) image shows very pure polycrystalline MgB2. A high resolution grain boundary image is shown in Figure 3(b). The interface is very clean and well connected. The indexed fast Fourier transform (FFT) pattern indicates that the right part parallels the (1 1 0) plane. The micro structure of SiC-MgB2 is similar with that of pure MgB2 with high density of defects. Furthermore, nanosize SiC particle are detected in the MgB2 matrix as indicated in Figure 3(c). Figure 3(d) shows the interface of SiC and MgB2. Based on the FFT analysis, the interface is marked with a dashed line on the image. The left side is a SiC grain paralleling the (1 0 1) plane and the right side is a MgB2 grain paralleling the (0 0 1) plane. This kind of interface will impose tensile stress along the *c*-axis in MgB2 because the thermal expansion coefficient for MgB2 is highly anisotropic in the [001] direction, while that for SiC is nearly isotropic, which is responsible for the enlarged *c*-axis of MgB2.

shown in the inset of Figure 2(a). The *α*SiC decreases slightly from 5×10-6/K at 1123 K to 2.5×10-6/

**Figure 2.** (a) Thermal expansion coefficients (*α*) along the a-axis and c-axis for MgB2 and SiC as a function of tempera‐ ture. The averaged *α*(T) values for MgB2 and SiC are plotted in the inset. (b) Plots of the normalized lattice changes for

MgB2 and SiC, and the thermal strain in the matrix during cooling from 1123 K to 0 K.

*α*(*T*), the normalized lattice change and lattice strain in the MgB2 matrix of SiC-MgB2 composite during cooling from 1123 K to 0 K can be derived, as shown in Figure 2(b). An assumption of Figure 2(b) is that the two phases are strongly connected and the volume shrinkage of MgB2 is confined by the relatively stable SiC. The normalized lattice strain is estimated to be -0.55% in SiC-MgB2 along the *c-*axis at room temperature. The negative value corresponds to tensile strain in the MgB2. The large *c*-axis strain in the doped MgB2 results in an enlargement in the *c*-axis by 0.15 % in comparison with pure MgB2. As estimated from the Williamson-Hall model [112], the lattice strain is 0.208 and 0.306 along the *a-*axis, and 0.292 and 1.13 along the *c-*axis for pure and SiC-MgB2, respectively. The lattice strain along the *c-*axis in the SiC-MgB2 has increased from that of pure MgB2 by a factor of 4, which is attributed to the high anisotropy

**Figure 3.** (a) Bright field TEM image of the pure MgB2 with indexed SAD pattern (inset). (b) High resolution electron mi‐ croscope (HREM) image of interface in pure MgB2 with FFT pattern along the [100] axis (inset). (c) Bright field TEM im‐ age of SiC-MgB2. (d) HREM image of interface in SiC-MgB2 and FFT patterns of SiC and MgB2 from each side of the

drops quickly from 1.7×10-5/K at 1123 K to zero at 0 K. Based on

K at 0 K, whereas the *α*MgB2

100 Superconductors – New Developments

in the thermal expansion coefficient of MgB2.

interface. The dashed line shows the interface of SiC and MgB2.

**Figure 4.** The magnetic *Jc* versus field at 5 K, 20 K, and 30 K for pure and nano-SiC doped samples. The inset shows the superconducting transitions of the two samples [103].

Based on the collective pinning model, [113], *Jc* is independent of the applied field in the singlevortex pinning regime (low magnetic field region: *H* < *Hsb*), where *Hsb* is the crossover field from single-vortex to small-bundle pinning. The *Jc* decreases exponentially in the small-bundle regime (high magnetic field: *Hsb* < *H < Hirr*). According to the dual model [14], the significant effect of SiC doping on *Jc* comes from the high level of C substitution on the B planes, which is responsible for the reduction of the self-field *Jc*[104, 105]. However, the SiC-MgB2 composite sample shows not only an improved in-field *Jc*, but also no degradation in self-field *Jc*, as indicated in Figure 4. The approximate *Hsb* values are also indicated on the *Jc* curves for 20 K and 30 K, although *Hsb* has not been detected at 5 K due to the relatively high supercurrents. The *in-situ* processed SiC doped MgB2 normally shows a decrease in *Tc* of 1.5 to 2 K, [14, 104, 105], but this present SiC-MgB2 composite sample features a small drop of 0.6 K, as shown in the inset of Figure 4. This phenomenon is attributed to the absence of any reaction between Mg and SiC, as well as the stretched MgB2 lattice, as indicated by the XRD pattern [107].

To investigate whether the lattice strain is significant in SiC-MgB2 during low temperature measurements to obtain *M*(*H*) and *M*(*T*) curves, Raman spectra were collected before and after the measurements. The Raman spectra for the pure MgB2 are shown in Figure 5(a) and (b) to compare the cooling effects on the matrix. Both the spectra have been fitted with three peaks: *ω*1, *ω*2, and *ω*<sup>3</sup> [114-116]. Based on the previous results, *ω*2 is the reflection of the *E*2*<sup>g</sup>* mode at the Г point of the Brillouin zone in the simple hexagonal MgB2 structure (space group: *P*6/ *mmm*), while *ω*1 and *ω*3 come from the lattice distortion. The effects of *ω*1 are not discussed in the following analysis because of its small influence on the spectra. As indicated by the fitting parameters that are shown in Figure 5, both the peak centers and the full width at half maximum (FWHM) values show negligible differences before and after the low temperature measurements because of synchronic volume fluctuation. The weak temperature dependence of the Raman spectra for pure MgB2 is in agreement with the results of Shi *et al* [117]. The *ω*<sup>2</sup> peak of the Raman spectrum of SiC-MgB2 before the low temperature measurement has shifted to the low frequency of 585 cm-1, as shown in Figure 6(a). The FWHM of the *ω*2 peak increases from ~200 cm-1 to 210 cm-1. Furthermore, the FWHM of the *ω*3 peak increases from ~93 cm-1 to 125 cm-1. The variations in both the Raman shift and the FWHM indicate strong lattice strain in the SiC-MgB2 composite. Figure 6(b) shows the cooling effect on the Raman spectrum of SiC-MgB2. The FWHM of the *ω*2 peak further increases to 228 cm-1, and the frequency of the *ω*<sup>3</sup> peak shifts to 770 cm-1. These results suggest that the stress field is very strong during the low temperature measurements in the SiC-MgB2 composite. Considering the stable defect struc‐ tures in the sample at room temperature and the measurement temperatures, the high *Jc* performance is attributed to the thermal strain. Although the interface or grain boundaries themselves are effective flux pinning centers, the thermal strain provides more efficient flux pinning force, based on the comparison of the *Jc* values in pure the MgB2 and the SiC-MgB2 composite.

It should be noted that the broadened *ω*2 peak in SiC-MgB2 is a signal of strong electron-*E*2*<sup>g</sup>* coupling, which is responsible for the high *Tc* in MgB2. The electron-*E*2*<sup>g</sup>* coupling constant is estimated from the Allen equation [118]: *Γ*<sup>2</sup> =2*πλE*2*<sup>g</sup> N* (0)*ωE*2*<sup>g</sup>* <sup>2</sup> , where Γ2 is the *ω*2 linewidth, *λE*2*<sup>g</sup>* is the strength of the electron-*E*2*<sup>g</sup>* coupling, and *N*(0) is the density of states on the Fermi surface. The experimental phonon frequency and linewidth are simply and directly related to the electron-phonon coupling constant (EPC), *λE*2*<sup>g</sup>* . The total density of states (DOS) at the Fermi energy, *E*F, of pure MgB2 is taken as 0*.*354 states*/*eV/cell/spin. The *σ* band contribution is 0.15 and the *π* band is 0.204 [119]. *N*(0) is assumed to be constant for the small changes of electrons

effect of SiC doping on *Jc* comes from the high level of C substitution on the B planes, which is responsible for the reduction of the self-field *Jc*[104, 105]. However, the SiC-MgB2 composite sample shows not only an improved in-field *Jc*, but also no degradation in self-field *Jc*, as indicated in Figure 4. The approximate *Hsb* values are also indicated on the *Jc* curves for 20 K and 30 K, although *Hsb* has not been detected at 5 K due to the relatively high supercurrents. The *in-situ* processed SiC doped MgB2 normally shows a decrease in *Tc* of 1.5 to 2 K, [14, 104, 105], but this present SiC-MgB2 composite sample features a small drop of 0.6 K, as shown in the inset of Figure 4. This phenomenon is attributed to the absence of any reaction between Mg and SiC, as well as the stretched MgB2 lattice, as indicated by the XRD pattern [107].

To investigate whether the lattice strain is significant in SiC-MgB2 during low temperature measurements to obtain *M*(*H*) and *M*(*T*) curves, Raman spectra were collected before and after the measurements. The Raman spectra for the pure MgB2 are shown in Figure 5(a) and (b) to compare the cooling effects on the matrix. Both the spectra have been fitted with three peaks: *ω*1, *ω*2, and *ω*<sup>3</sup> [114-116]. Based on the previous results, *ω*2 is the reflection of the *E*2*<sup>g</sup>* mode at the Г point of the Brillouin zone in the simple hexagonal MgB2 structure (space group: *P*6/ *mmm*), while *ω*1 and *ω*3 come from the lattice distortion. The effects of *ω*1 are not discussed in the following analysis because of its small influence on the spectra. As indicated by the fitting parameters that are shown in Figure 5, both the peak centers and the full width at half maximum (FWHM) values show negligible differences before and after the low temperature measurements because of synchronic volume fluctuation. The weak temperature dependence of the Raman spectra for pure MgB2 is in agreement with the results of Shi *et al* [117]. The *ω*<sup>2</sup> peak of the Raman spectrum of SiC-MgB2 before the low temperature measurement has shifted to the low frequency of 585 cm-1, as shown in Figure 6(a). The FWHM of the *ω*2 peak increases from ~200 cm-1 to 210 cm-1. Furthermore, the FWHM of the *ω*3 peak increases from ~93 cm-1 to 125 cm-1. The variations in both the Raman shift and the FWHM indicate strong lattice strain in the SiC-MgB2 composite. Figure 6(b) shows the cooling effect on the Raman spectrum of SiC-MgB2. The FWHM of the *ω*2 peak further increases to 228 cm-1, and the frequency of the *ω*<sup>3</sup> peak shifts to 770 cm-1. These results suggest that the stress field is very strong during the low temperature measurements in the SiC-MgB2 composite. Considering the stable defect struc‐ tures in the sample at room temperature and the measurement temperatures, the high *Jc* performance is attributed to the thermal strain. Although the interface or grain boundaries themselves are effective flux pinning centers, the thermal strain provides more efficient flux pinning force, based on the comparison of the *Jc* values in pure the MgB2 and the SiC-MgB2

It should be noted that the broadened *ω*2 peak in SiC-MgB2 is a signal of strong electron-*E*2*<sup>g</sup>* coupling, which is responsible for the high *Tc* in MgB2. The electron-*E*2*<sup>g</sup>* coupling constant is

is the strength of the electron-*E*2*<sup>g</sup>* coupling, and *N*(0) is the density of states on the Fermi surface. The experimental phonon frequency and linewidth are simply and directly related to the

energy, *E*F, of pure MgB2 is taken as 0*.*354 states*/*eV/cell/spin. The *σ* band contribution is 0.15 and the *π* band is 0.204 [119]. *N*(0) is assumed to be constant for the small changes of electrons

*N* (0)*ωE*2*<sup>g</sup>*

<sup>2</sup> , where Γ2 is the *ω*2 linewidth, *λE*2*<sup>g</sup>*

. The total density of states (DOS) at the Fermi

composite.

102 Superconductors – New Developments

estimated from the Allen equation [118]: *Γ*<sup>2</sup> =2*πλE*2*<sup>g</sup>*

electron-phonon coupling constant (EPC), *λE*2*<sup>g</sup>*

**Figure 5.** Fitting and experimental results for the normalized ambient Raman spectrum of MgB2 sintered at 850 o C for 10 h (a), and the cooling effect on the Raman spectrum (b) [103].

**Figure 6.** Fitting and experimental results for the normalized ambient Raman spectrum of SiC-MgB2 sintered at 850 o C for 10 h (a), and the cooling effect on the Raman spectrum (b) [103].

and holes in MgB2 and SiC-MgB2. Taking the fitting values of the *ω*<sup>2</sup> peaks with cooling effects, the *λE*2*<sup>g</sup>* values for the pure MgB2 and SiC-MgB2 are 2.327 and 2.706, respectively. The *λE*2*<sup>g</sup>* of SiC-MgB2 is just slightly higher than that of the pure MgB2. However, the *Tc* of SiC-MgB2 is slightly decreased compared to that of the pure MgB2. The total EPC constants are degraded by the scattering effects of SiC impurities in the MgB2 matrix, which can be estimated with the McMillan formula [120], as modified by Allen and Dynes:[121] *Tc* <sup>=</sup> *<sup>ω</sup>*log 1.2 exp( <sup>−</sup> 1.04(1 <sup>+</sup> *<sup>λ</sup>*) *λ* − *μ* \* (1 <sup>+</sup> 0.62*λ*) ), where *ω*log =(390×*ωE*2*<sup>g</sup>* <sup>2</sup> ×690) is the averaged phonon frequency [122], with 390 and 690 cm-1  being the phonon frequencies of the other modes in the MgB2 system [123], *μ*\* is the Coulomb pseudopotential, taken as equal to 0.13 [124], and *λ* is the total EPC constant. Taking these values, *λ* is calculated as 0.888 in pure MgB2 and 0.886 in SiC-MgB2, respectively. Although the values are very similar, the *λ* of MgB2 is a little higher because of its low impurity scattering effects. It should be noted that the *λ* values were overestimated using the McMillan formula for the two-gap nature of MgB2. However, the overestimations do not change the dependence of *λ* on the strain effect due to the main contribution of the *σ*-band. The residual resistivity of SiC-MgB2 is 16 *μ*Ω cm, but it is just 12 *μ*Ω cm for pure MgB2, due to the weak impurity scattering effects.

In summary, the thermal strain originating from the interface of SiC and MgB2 is one of the most effective sources of flux pinning centers to improve the supercurrent critical density. The weak temperature dependence of the thermal expansion coefficient of SiC stretches the MgB2 lattice as the temperature decreases. The thermal strain supplies much more effective flux pinning force than the interfaces and grain boundaries themselves. The low temperature effects on Raman spectra include very strong lattice stretching at the application temperature of MgB2, which has benefits from both the *Jc* and the *Tc* behaviors.

### **3. High connectivity MgB2 wires fabricated by combined** *in-situ***/***ex-situ* **process**

The self-field critical current density, *Jc*(0), of MgB2 is much higher than for pure or doped samples processed with *in-situ* annealing [75, 81, 125-128]. *Jc*(0) values have been reported as high as 3.5×107 A/cm2 at 4.2 K and 1.6×108 A/cm2 at 2 K in highly connected thin films made by HPCVD [129, 130]. The connectivity is much lower than the theoretical value in *in-situ* MgB2 because the technique involves a liquid-solid phase reaction process with considerable shrinkage due to the high density of MgB2 compared to the powder mixture of Mg and B [104, 115]. Although the diffusion process could increase the *Jc* of bulk samples, the *Jc*(0) and disorder of wires and tapes cannot be improved using similar methods. Several research groups have reported possible techniques to increase the connectivity of *in-situ* filamentary tapes. High pressure sintering and cold high pressure densification (CHPD) can make it possible to fabricate high density wire and tape samples [96, 131, 132]. Nevertheless, neither HIP nor CHPD are suitable for long MgB2 wires and tapes, and the *Jc* values are still lower than needed for practical application. Kováč et al. reported a mixed *in-situ*/*ex-situ* process to make MgB2 wires, and it was found that the *Jc* was increased when the *ex-situ* powder ratio were 23% and 50% [133]. They used commercial MgB2 powder from Alfa Aesar in this process with a very wide grain size distribution ranging from submicrometer size up to 100 *μ*m. In this work, high quality home-made *ex-situ* powder was used to repeat the mixed *in-situ*/*ex-situ* process to develop MgB2/Fe wires with high connectivity and strong disorder to increase both the low and high field *Jc* properties [134]. The home-made powder was fabricated through low temperature annealing, and the particle size was homogeneous and as small as ~200 nm. The *Jc* dependence on microstruc‐ ture, connectivity, and disorder in MgB2 wires was analyzed based on the microstructure observations.

 being the phonon frequencies of the other modes in the MgB2 system [123], *μ*\* is the Coulomb pseudopotential, taken as equal to 0.13 [124], and *λ* is the total EPC constant. Taking these values, *λ* is calculated as 0.888 in pure MgB2 and 0.886 in SiC-MgB2, respectively. Although the values are very similar, the *λ* of MgB2 is a little higher because of its low impurity scattering effects. It should be noted that the *λ* values were overestimated using the McMillan formula for the two-gap nature of MgB2. However, the overestimations do not change the dependence of *λ* on the strain effect due to the main contribution of the *σ*-band. The residual resistivity of SiC-MgB2 is 16 *μ*Ω cm, but it is just 12 *μ*Ω cm for pure MgB2, due to the weak impurity scattering

In summary, the thermal strain originating from the interface of SiC and MgB2 is one of the most effective sources of flux pinning centers to improve the supercurrent critical density. The weak temperature dependence of the thermal expansion coefficient of SiC stretches the MgB2 lattice as the temperature decreases. The thermal strain supplies much more effective flux pinning force than the interfaces and grain boundaries themselves. The low temperature effects on Raman spectra include very strong lattice stretching at the application temperature

**3. High connectivity MgB2 wires fabricated by combined** *in-situ***/***ex-situ*

The self-field critical current density, *Jc*(0), of MgB2 is much higher than for pure or doped samples processed with *in-situ* annealing [75, 81, 125-128]. *Jc*(0) values have been reported as high as 3.5×107 A/cm2 at 4.2 K and 1.6×108 A/cm2 at 2 K in highly connected thin films made by HPCVD [129, 130]. The connectivity is much lower than the theoretical value in *in-situ* MgB2 because the technique involves a liquid-solid phase reaction process with considerable shrinkage due to the high density of MgB2 compared to the powder mixture of Mg and B [104, 115]. Although the diffusion process could increase the *Jc* of bulk samples, the *Jc*(0) and disorder of wires and tapes cannot be improved using similar methods. Several research groups have reported possible techniques to increase the connectivity of *in-situ* filamentary tapes. High pressure sintering and cold high pressure densification (CHPD) can make it possible to fabricate high density wire and tape samples [96, 131, 132]. Nevertheless, neither HIP nor CHPD are suitable for long MgB2 wires and tapes, and the *Jc* values are still lower than needed for practical application. Kováč et al. reported a mixed *in-situ*/*ex-situ* process to make MgB2 wires, and it was found that the *Jc* was increased when the *ex-situ* powder ratio were 23% and 50% [133]. They used commercial MgB2 powder from Alfa Aesar in this process with a very wide grain size distribution ranging from submicrometer size up to 100 *μ*m. In this work, high quality home-made *ex-situ* powder was used to repeat the mixed *in-situ*/*ex-situ* process to develop MgB2/Fe wires with high connectivity and strong disorder to increase both the low and high field *Jc* properties [134]. The home-made powder was fabricated through low temperature annealing, and the particle size was homogeneous and as small as ~200 nm. The *Jc* dependence on microstruc‐

of MgB2, which has benefits from both the *Jc* and the *Tc* behaviors.

effects.

104 Superconductors – New Developments

**process**

MgB2 wires were fabricated by the powder-in-tube (PIT) process using a ball-milled mixture of Mg (99%) and amorphous B (99%). The *in-situ* wires were sintered at 750, 850, 950, and 1050 °C for 30 min in high purity Ar and marked as 750in, 850in, 950in, and 1050in, respectively. The *in-situ* MgB2 powder was sintered at 650 °C for 30 min in high purity Ar flow and then ball-milled. Then the PIT method was employed to fabricate *in-situ*/*ex-situ* combined MgB2/Fe wires using 1:3 ratio of precursor powders to form a mixture of Mg and B powders. All the green wires were annealed at 750, 850, 950, and 1050 °C for 30 min in high purity Ar and marked as 750inex, 850inex, 950inex, and 1050inex, respectively.

The phases and microstructure were characterized by XRD (D/max-2200) and field emission gun scanning electron microscopy (FEG-SEM: JSM-6700F) at room temperature. The super‐ conducting properties were detected from 5 K to 305 K using a Physical Properties Measure‐ ment System (PPMS: Quantum Design). The critical superconducting transition temperature, *Tc*, is defined as the onset point on the magnetic moment *vs.* temperature curve, *M*(*T*), measured in a magnetic field of 25 Oe. The magnetic *Jc* was derived from the Bean model. The resistivity dependence on applied magnetic field and temperature, *ρ*(*H*, *T*), was measured using the fourprobe method with *H* from 0 T to 13 T applied perpendicularly to the current direction, from 5 K to 305 K. *Hc*2 and *Hirr* were defined as the magnetic field values at 90% and 10% on the superconducting transition on the *ρ*(*H*, *T*) curve, respectively. The active connectivity factor, *AF*, was calculated based on the *ρ*(*H*, *T*) behavior.

**Figure 7.** *Tc* dependence on sintering temperatures. The insets display the normalized magnetic moment dependence on measurement temperature for *in-situ* samples (upper) and for combined *in-situ*/*ex-situ* samples (lower) [134].

According to the indexed XRD patterns, the samples contain a small amount of MgO. The MgO contents are high in 950in, 1050in, and 1050exin compared with the other samples. The broad transition widths from the normal state to the superconducting state of these samples confirm the high impurity contents, as shown in the insets of Figure 7. The 1050in transition width is ~7 K compared with the width of ~2 K for the other samples, which is attributed to the degraded connectivity of the magnetic flux due to the high MgO content. The *in-situ* sintered samples show higher *Tc* values by 0.5 – 1 K compared with the *in-situ*/*ex-situ* ones. The *Tc* of 1050in is similar to that of 1050inex because of the high amount of impurity phase. Ball milling of the raw materials induces a great amount of defects in the *in-situ*/*ex-situ* samples, which display lower *Tc* compared with the *in-situ* samples [135, 136]. The connectivity of the *in-situ*/*ex-situ* samples is worse than those of the *in-situ* samples judging from their big transition widths. The low amount of Mg evaporation may be responsible for the narrow transition width of 1050inex compared with that of 1050in because the stable precursor MgB2 and low quantity of Mg in the raw materials reduce the magnesium loss during the sintering at 1050 o C.

Typical SEM images of the *in-situ* samples are shown in Figure 8. The grain size of 750in is about 300 nm, and the grains show an isolated distribution due to independent growth. 850in, 950in, and 1050in have big clusters of grains because the increasing sintering temperatures have extended the crystal growth time. Some clusters are as big as 1 *μ*m in 1050in. The crystallinity is enhanced at higher sintering temperatures. A high sintering temperature induces raw magnesium evaporation and MgO formation, which can be observed as small white particles without contrast under SEM in 1050in.

The crystal shapes for the *in-situ*/*ex-situ* samples are irregular with a dispersed distribution of grain sizea, as shown in Figure 9. The grain size of 750inex is small because of the low sintering temperature. The recrystallization effect is triggered for 850inex, 950inex, and 1050inex, and big grains as large as 1 *μ*m are observed. 1050in and 1050inex show similar microstructures because the high sintering temperature provides enough energy and a long time for the crystal growth.

**Figure 8.** SEM images for the *in-situ* samples sintered at (a) 750 o C, (b) 850 o C, (c) 950 o C, and (d) 1050 o C. The crystal growth was improved gradually with increasing sintering temperature.

Figure 10 compares the *Jc* dependence on applied magnetic field measured at 5 K and 20 K. The *Jc* value of 1050in is the worst because of the high MgO content. The *Jc* performances of

transition widths from the normal state to the superconducting state of these samples confirm the high impurity contents, as shown in the insets of Figure 7. The 1050in transition width is ~7 K compared with the width of ~2 K for the other samples, which is attributed to the degraded connectivity of the magnetic flux due to the high MgO content. The *in-situ* sintered samples show higher *Tc* values by 0.5 – 1 K compared with the *in-situ*/*ex-situ* ones. The *Tc* of 1050in is similar to that of 1050inex because of the high amount of impurity phase. Ball milling of the raw materials induces a great amount of defects in the *in-situ*/*ex-situ* samples, which display lower *Tc* compared with the *in-situ* samples [135, 136]. The connectivity of the *in-situ*/*ex-situ* samples is worse than those of the *in-situ* samples judging from their big transition widths. The low amount of Mg evaporation may be responsible for the narrow transition width of 1050inex compared with that of 1050in because the stable precursor MgB2 and low quantity of

Mg in the raw materials reduce the magnesium loss during the sintering at 1050 o

white particles without contrast under SEM in 1050in.

**Figure 8.** SEM images for the *in-situ* samples sintered at (a) 750 o

growth was improved gradually with increasing sintering temperature.

growth.

106 Superconductors – New Developments

Typical SEM images of the *in-situ* samples are shown in Figure 8. The grain size of 750in is about 300 nm, and the grains show an isolated distribution due to independent growth. 850in, 950in, and 1050in have big clusters of grains because the increasing sintering temperatures have extended the crystal growth time. Some clusters are as big as 1 *μ*m in 1050in. The crystallinity is enhanced at higher sintering temperatures. A high sintering temperature induces raw magnesium evaporation and MgO formation, which can be observed as small

The crystal shapes for the *in-situ*/*ex-situ* samples are irregular with a dispersed distribution of grain sizea, as shown in Figure 9. The grain size of 750inex is small because of the low sintering temperature. The recrystallization effect is triggered for 850inex, 950inex, and 1050inex, and big grains as large as 1 *μ*m are observed. 1050in and 1050inex show similar microstructures because the high sintering temperature provides enough energy and a long time for the crystal

C, (b) 850 o

Figure 10 compares the *Jc* dependence on applied magnetic field measured at 5 K and 20 K. The *Jc* value of 1050in is the worst because of the high MgO content. The *Jc* performances of

C, (c) 950 o

C, and (d) 1050 o

C. The crystal

C.

**Figure 9.** SEM images for the combined *in-situ*/*ex-situ* samples sintered at (a) 750 o C, (b) 850 o C, (c) 950 o C, and (d) 1050 o C. The grains are inhomogeneous due to the ball milled MgB2 precursor and the recrystallization effects.

750in, 850in, 750inex, and 1050inex are quite similar over the whole field range. While the *Jc* deteriorated in 950in and 1050in under higher magnetic fields. 850inex and 950inex show amazingly high *Jc* properties. The *Jc* values at 5 K under 8 T magnetic field are around five times higher than those of the best *in-situ* samples. The inset of Figure 10 compares the low field performances measured at 20 K. The *in-situ* samples, except for 1050in, show competitive low field *Jc*. The high crystal quality of 950in is of benefit for its high self-field *Jc* performance. 750inex and 850inex show low self-field *Jc* values. While 950inex and 1050inex display improved *Jc*, the values are lower than the self-field *Jc* of 950in due to the high MgO contents.

The *Jc* performance depends on the flux pinning mechanism under different magnetic field intensities. The collective pinning model classifies the disorder-induced spatial fluctuations in the vortex lattice into three regimes based on the strength the magnetic field: e.g. single-vortex, small-bundle, large-bundle, and charge-density-wave type relaxation of the vortex lattice [113]. The practicable *Jc* of MgB2 falls into the single-vortex pinning region and the small-bundle pinning region in the phase diagram. The connectivity determines the *Jc* performance in the single-vortex pinning regime because the effective charge carrier density is responsible for the self-field *Jc*, while *Hc*2 and *Hirr* are responsible for the *Jc* performance in the small-bundle regime based on the disorder or defects.

**Figure 10.** *Jc* dependence on applied magnetic field at 5 K and 20 K. The inset compares the self-field *Jc* behavior at 20 K [134].

A practical quantity to evaluate the connectivity is the active area fraction, *AF* [21],

$$\mathcal{A}\_{F} = \frac{\Delta\rho\_{\text{ideal}}}{\Delta\rho(\text{300K})},\tag{2}$$

where,

$$
\Delta \rho\_{\text{ideal}} = \rho\_{\text{ideal}} \left( \text{300K} \right) \ -\rho\_{\text{ideal}} \left( \text{40K} \right) \approx \text{9} \,\mu\text{\Omega cm},\tag{3}
$$

is the resistivity of fully connected MgB2 without any disorder [18], and

$$
\Delta\rho(\text{300}) = \rho(\text{300}K) - \rho(T\_c). \tag{4}
$$

**Figure 11.** *AF* dependence on sintering temperature. The short dashed line indicates *AF* = 0.175. The upper left inset compares the resistivity of the *in-situ* samples. The upper right inset compares the resistivity of the combined *insitu*/*ex-situ* samples [134].

Figure 11 compares the *AF* of all the samples. All the samples show lower connectivity compared with those of ideal crystals, as indicated by the low *AF* values. The *AF* value of 750in is just 0.169, and high sintering temperature enhances the connectivity. It is ~ 0.26 for 850in. Higher sintering temperatures than 850 o C can improve the *AF* slightly, which indicates that the connectivity is easy to improve for *in-situ* samples. Although the MgO content is high in 1050in, its high *AF* value is attributed to sufficient crystallization. However, its low magnetic field *Jc* was degraded by MgO. The combined *in-situ*/*ex-situ* samples show rather low *AF* values compared with the *in-situ* samples. The phenomenon is consistent with the high resistivity of the *in-situ*/*ex-situ* samples, as shown in the insets of Figure 11. The gradually improved connectivity improves the *AF* values for the *in-situ*/*ex-situ* samples due to the improved solid state reaction. The self-field *Jc* performances are also improved for 950inex and 1050inex.

A practical quantity to evaluate the connectivity is the active area fraction, *AF* [21],

D = D *AF*

D = rr

where,

108 Superconductors – New Developments

*situ*/*ex-situ* samples [134].

Higher sintering temperatures than 850 o

r

( ) ideal , 300K

(2)

 mideal ideal(300K – 40K 9 cm, ) ideal( ) » W (3)

(300 300 – . ) ( *K T* ) ( *<sup>c</sup>* ) (4)

C can improve the *AF* slightly, which indicates that

 r

**Figure 11.** *AF* dependence on sintering temperature. The short dashed line indicates *AF* = 0.175. The upper left inset compares the resistivity of the *in-situ* samples. The upper right inset compares the resistivity of the combined *in-*

Figure 11 compares the *AF* of all the samples. All the samples show lower connectivity compared with those of ideal crystals, as indicated by the low *AF* values. The *AF* value of 750in is just 0.169, and high sintering temperature enhances the connectivity. It is ~ 0.26 for 850in.

the connectivity is easy to improve for *in-situ* samples. Although the MgO content is high in 1050in, its high *AF* value is attributed to sufficient crystallization. However, its low magnetic field *Jc* was degraded by MgO. The combined *in-situ*/*ex-situ* samples show rather low *AF* values compared with the *in-situ* samples. The phenomenon is consistent with the high resistivity of the *in-situ*/*ex-situ* samples, as shown in the insets of Figure 11. The gradually improved

r

 r

is the resistivity of fully connected MgB2 without any disorder [18], and

D = rr The *Jc* performance in the small-bundle region depends on a strong flux pinning force. The flux pinning centers could be lattice distortion, most types of defects, and grain boundaries [110, 137]. The temperature dependences of *Hc*2 and *Hirr* determine the strength of the pinning force, as shown in Figure 12. The high field *Jc* performance is in agreement with the *Hc*2 and *Hirr* behavior. The 1050in sample shows the lowest *Hc*2 and *Hirr* among all the samples. 850inex and 950inex show the highest *Hc*2 and *Hirr*, which are consistent with their high *Jc* values in the smallbundle region. The *ex-situ* powder induces strong disorder and proper crystallization, which are responsible for the high *Hc*2 and *Hirr* values.

**Figure 12.** *Hc*2 and *Hirr* of (a) the *in-situ* samples and (b) the combined *in-situ*/*ex-situ* samples [134].

In summary, both connectivity and disorder show strong influences on the *Jc* properties of MgB2. The connectivity is responsible for the high effective charge carrier density, which determines the self-field *Jc* performance. The strong flux pinning force induced by defects and disorder is responsible for the promising *Jc* in high magnetic field. The enhanced *Jc* perform‐ ances of 850inex and 950inex are attributed to the optimized connectivity and disorder. The *Jc* values obtained in this work are still far below the *Jd* value, ~8.7×108 A/cm2 for pure MgB2. The *Jc* improvement in MgB2 should be explored based on the chemical doping effects and combined *in-situ*/*ex-situ* process.

#### **4. Nano-SiC doped MgB2 wires made by combined** *In-Situ***/***Ex-Situ* **process**

The combined *in-situ*/*ex-situ* process has proved to be a promising technique for the fabrication of practical MgB2 wires. The *Jc* of MgB2 superconductors has been enhanced through many different kinds of dopants or additives [125], especially different carbon sources [75, 81, 1 2 126-128, 138, 139]. In this work, a mixed *in-situ*/*ex-situ* technique was employed to develop nano-SiC doped MgB2 wires with high connectivity and strong flux pinning force to increase both the low and high field *Jc* properties [140]. The SiC particle size is another critical issue for introducing strong flux pinning forces into MgB2. The size of SiC used in this work is smaller than the sizes used in previous research, and the *Jc* dependence on sintering temperature also shows a very different trend [81, 104, 141, 142].

The powder-in-tube (PIT) process was employed to make practical MgB2 wires from a ballmilled mixture of Mg (99%), B (99%, amorphous), and SiC (< 15 nm).]The sample fabrication and characterization are similar to the techniques mentioned for the pure samples in the last section.

Running Title <sup>13</sup>

Figure 13. XRD patterns of nano-SiC doped MgB2 3 /Fe wires fabricated by (a) the *in-situ* technique and (b) the *in-situ*/*ex-situ* technique, with sintering at 750, 850, 950, and 1050 <sup>o</sup> 4 C, respectively. All patterns were indexed with MgB2 5 , MgO, Mg2Si, SiC, and Mg.[140] **Figure 13.** XRD patterns of nano-SiC doped MgB2/Fe wires fabricated by (a) the *in-situ* technique and (b) the *in-situ*/*exsitu* technique, with sintering at 750, 850, 950, and 1050 o C, respectively. All patterns were indexed with MgB2, MgO, Mg2Si, SiC, and Mg [140].

6 Figure13 shows the XRD patterns of the two batches of samples. According to the indexed XRD patterns, all samples show quite high purity of MgB2 7 with small amounts of MgO and un-reacted Mg 8 and SiC. The un-reacted Mg can be detected because of the high content of SiC in the raw 9 materials.[104, 115, 143] The most interesting phase change relates to change in the Mg2Si content 10 with sintering temperature. 750in shows very high Mg2Si content, which decreases with the sintering 11 temperature and becomes a trace peak in 1050in. However, more than a trace of Mg2Si can only be 12 found in samples sintered at lower temperature using the combined *in-situ*/*ex-situ* method, 750inex 13 and 850inex. The variation of Mg2Si content is an important signal of the C and Si distribution in the MgB2 14 matrix. Figure 14 shows the SEM images of 850in and 850inex. The 850in sample contains big-size slits between MgB2 15 clusters due to the volume contraction during *in-situ* sintering of Mg and B powders. The 850inex sample shows hard-packed MgB2 16 clusters because the *ex-situ* precursor is nucleating center and release the strain of the *in-situ* MgB2 17 . The critical transition temperatures (*Tc* 18 ) of the two batches of samples are compared in Figure 15. It is found that the *Tc* 19 values of the *in-situ* sintered samples are always a slightly lower than those for the samples from the other batch, except for 1050in, and the *Tc* 20 dependence on sintering temperature of Figure13 shows the XRD patterns of the two batches of samples. According to the indexed XRD patterns, all samples show quite high purity of MgB2, with only small amounts of MgO and un-reacted Mg and SiC. The un-reacted Mg can be detected because of the high content of SiC in the raw materials [104, 115, 143]. The most interesting phase change relates to the change in the Mg2Si content with sintering temperature. 750in shows very high Mg2Si content, which decreases with increasing sintering temperature and becomes a trace peak in 1050in. However, more than a trace of Mg2Si can only be found in samples sintered at lower temper‐ ature using the combined *in-situ*/*ex-situ* method, 750inex and 850inex. The variation of Mg2Si content is an important signal of the C and Si distributions in the MgB2 matrix. Figure 14 shows SEM images of 850in and 850inex. The 850in sample contains large slits between MgB2 clusters due to the volume contraction during the *in-situ* sintering of Mg and B powders. The 850inex sample shows hard-packed MgB2 clusters because the *ex-situ* precursor is a course of nucleating centers and releases the strain of the *in-situ* MgB2.

the two batches of samples is exactly the same, which means that the *Tc* 21 depends greatly on the 22 sintering temperature, but not on the different techniques. However, the transition widths from the 23 normal state to the superconducting state are quite different for the two batches of samples, as shown 24 in the inset of Figure 15. The transition widths of the *in-situ* sintered samples are quite broad 25 compared with those fabricated by the combined technique. The transition width is about 4 K for 26 750in and becomes 3 K in the 850in and 950in samples sintered at higher temperature due to the high The critical transition temperatures (*Tc*) of the two batches of samples are compared in Figure 15. It is found that the *Tc* values of the *in-situ* sintered samples are always slightly lower than those for the samples from the other batch, except for 1050in, and the *Tc* dependence on sintering temperature of the two batches of samples is exactly the same, which means that the

 crystallinity. It should be noted that the transition of 1050in shows a two-step behaviour, which may be attributed to the inhomogeneous carbon substitution effect or the inhomogeneous SiC distribution in the raw materials. The transition widths of all the samples made by the *in-situ*/*ex-situ* combined technique are 2.5 K, showing behaviour that is independent of the sintering temperature. This means that the crystallinity is increased through the *in-situ*/*ex-situ* combined technique because the precursor MgB2 powder is a source of high quality nucleating centres for newly formed MgB2 32 during the solid-

33 liquid reaction between magnesium and boron.

*Tc* depends greatly on the sintering temperature, but not on the different techniques. However, the transition widths from the normal state to the superconducting state are quite different for the two batches of samples, as shown in the inset of Figure 15. The transition widths of the *insitu* sintered samples are quite broad compared with those fabricated by the combined technique. The transition width is about 4 K for 750in and becomes 3 K for the 850in and 950in samples sintered at higher temperature due to the high crystallinity. It should be noted that the transition of 1050in shows a two-step behaviour, which may be attributed to the inhomo‐ geneous carbon substitution effect or the inhomogeneous SiC distribution in the raw materials. The transition widths of all the samples made by the *in-situ*/*ex-situ* combined technique are 2.5 K, showing behaviour that is independent of the sintering temperature. This means that the crystallinity is increased through the *in-situ*/*ex-situ* combined technique because the precursor MgB2 powder is a source of high quality nucleating centres for the newly formed MgB2 during the solid-liquid reaction between the magnesium and the boron.

**Figure 14.** SEM photos of (a) 850in and (b) 850inex [140].

126-128, 138, 139]. In this work, a mixed *in-situ*/*ex-situ* technique was employed to develop nano-SiC doped MgB2 wires with high connectivity and strong flux pinning force to increase both the low and high field *Jc* properties [140]. The SiC particle size is another critical issue for introducing strong flux pinning forces into MgB2. The size of SiC used in this work is smaller than the sizes used in previous research, and the *Jc* dependence on sintering temperature also

The powder-in-tube (PIT) process was employed to make practical MgB2 wires from a ballmilled mixture of Mg (99%), B (99%, amorphous), and SiC (< 15 nm).]The sample fabrication and characterization are similar to the techniques mentioned for the pure samples in the last

Running Title <sup>13</sup>

Figure 13. XRD patterns of nano-SiC doped MgB2 3 /Fe wires fabricated by (a) the *in-situ* technique and (b) the *in-situ*/*ex-situ* technique, with sintering at 750, 850, 950, and 1050 <sup>o</sup> 4 C, respectively. All

**Figure 13.** XRD patterns of nano-SiC doped MgB2/Fe wires fabricated by (a) the *in-situ* technique and (b) the *in-situ*/*ex-*

Figure13 shows the XRD patterns of the two batches of samples. According to the indexed XRD patterns, all samples show quite high purity of MgB2, with only small amounts of MgO and un-reacted Mg and SiC. The un-reacted Mg can be detected because of the high content of SiC in the raw materials [104, 115, 143]. The most interesting phase change relates to the change in the Mg2Si content with sintering temperature. 750in shows very high Mg2Si content, which decreases with increasing sintering temperature and becomes a trace peak in 1050in. However, more than a trace of Mg2Si can only be found in samples sintered at lower temper‐ ature using the combined *in-situ*/*ex-situ* method, 750inex and 850inex. The variation of Mg2Si content is an important signal of the C and Si distributions in the MgB2 matrix. Figure 14 shows SEM images of 850in and 850inex. The 850in sample contains large slits between MgB2 clusters due to the volume contraction during the *in-situ* sintering of Mg and B powders. The 850inex sample shows hard-packed MgB2 clusters because the *ex-situ* precursor is a course of nucleating

C, respectively. All patterns were indexed with MgB2, MgO,

 Figure13 shows the XRD patterns of the two batches of samples. According to the indexed XRD patterns, all samples show quite high purity of MgB2 7 with small amounts of MgO and un-reacted Mg and SiC. The un-reacted Mg can be detected because of the high content of SiC in the raw materials.[104, 115, 143] The most interesting phase change relates to change in the Mg2Si content with sintering temperature. 750in shows very high Mg2Si content, which decreases with the sintering temperature and becomes a trace peak in 1050in. However, more than a trace of Mg2Si can only be found in samples sintered at lower temperature using the combined *in-situ*/*ex-situ* method, 750inex and 850inex. The variation of Mg2Si content is an important signal of the C and Si distribution in the MgB2 14 matrix. Figure 14 shows the SEM images of 850in and 850inex. The 850in sample contains big-size slits between MgB2 15 clusters due to the volume contraction during *in-situ* sintering of Mg and B powders. The 850inex sample shows hard-packed MgB2 16 clusters because the *ex-situ* precursor is

The critical transition temperatures (*Tc* 18 ) of the two batches of samples are compared in Figure 15. It is found that the *Tc* 19 values of the *in-situ* sintered samples are always a slightly lower than those for the samples from the other batch, except for 1050in, and the *Tc* 20 dependence on sintering temperature of the two batches of samples is exactly the same, which means that the *Tc* 21 depends greatly on the sintering temperature, but not on the different techniques. However, the transition widths from the normal state to the superconducting state are quite different for the two batches of samples, as shown in the inset of Figure 15. The transition widths of the *in-situ* sintered samples are quite broad compared with those fabricated by the combined technique. The transition width is about 4 K for 750in and becomes 3 K in the 850in and 950in samples sintered at higher temperature due to the high crystallinity. It should be noted that the transition of 1050in shows a two-step behaviour, which may be attributed to the inhomogeneous carbon substitution effect or the inhomogeneous SiC distribution in the raw materials. The transition widths of all the samples made by the *in-situ*/*ex-situ* combined technique are 2.5 K, showing behaviour that is independent of the sintering temperature. This means that the crystallinity is increased through the *in-situ*/*ex-situ* combined technique because the precursor MgB2 powder is a source of high quality nucleating centres for newly formed MgB2 32 during the solid-

The critical transition temperatures (*Tc*) of the two batches of samples are compared in Figure 15. It is found that the *Tc* values of the *in-situ* sintered samples are always slightly lower than those for the samples from the other batch, except for 1050in, and the *Tc* dependence on sintering temperature of the two batches of samples is exactly the same, which means that the

shows a very different trend [81, 104, 141, 142].

110 Superconductors – New Developments

patterns were indexed with MgB2 5 , MgO, Mg2Si, SiC, and Mg.[140]

*situ* technique, with sintering at 750, 850, 950, and 1050 o

Mg2Si, SiC, and Mg [140].

nucleating center and release the strain of the *in-situ* MgB2 17 .

centers and releases the strain of the *in-situ* MgB2.

33 liquid reaction between magnesium and boron.

section.

1 2

**Figure 15.** *Tc* dependence on sintering temperature. The insets show the normalized magnetic moment dependence on the measuring temperature for the *in-situ* samples (upper) and for the *in-situ*/*ex-situ* samples (lower) [140].

The *Jc* dependence on the applied field is shown in Figure 16 for typical samples, which were measured at 5 K and 20 K, respectively. It should be noted that the *Jc* dependence on sintering temperature in this work is totally different from previously reported results, because the solidliquid reaction dynamics is different due to the small SiC particle size, less than 15 nm, which is much smaller than the particle sizes used before. The *Jc* benefits from the high sintering temperature. 750in, 850in, and 750inex display non-competitive performance over the whole field range. 1050inex has very high low field *Jc* values but its *Jc* deteriorates with increasing magnetic field. The *Jc* properties of 950in, 850inex, and 950inex show outstandingly high *Jc* performances among all the samples. It is concluded that the *in-situ*/*ex-situ* combined technique only requires a lower sintering temperature to achieve high quality MgB2 wires, which is very important for industrial application in terms of energy saving and equipment simplification. The *Jc* values of 750inex are double those of 750in at 5 K and 20 K over the measured magnetic field range. The inset of Figure 16 displays the low field performances at 20 K to avoid the influence of the flux jumping effect. 750in and 750inex show quite low *Jc* values in lower magnetic field. 1050in and 850inex show competitive self-field *Jc*. The ball-milling process used to produce the *ex-situ* MgB2 powder destroyes the porous structure and enhances the density of MgB2 fabricated by the *in-situ*/*ex-situ* combined process. This is because of the small particle size of SiC used in this work, which induces different reaction dynamics during the *in-situ* or *in-situ*/*ex-situ* processing [81, 104, 141, 142], so that the present *Jc* dependence on sintering temperature is quite different from what has been previously reported. It is proposed that the liquid Mg reacts with SiC first to form Mg2Si and releases free C at low sintering temperature. Then the Mg2Si reacts with B to form MgB2 and releases free Si at high sintering temperatures. Both C and Si have very small sizes and cannot be detected by XRD. The coherence length, ξ, of MgB2 is anisotropic. *ξ*ab(0) = 3.7 – 12 nm, and *ξ*c(0) = 1.6 - 3.6 nm [110], which is shorter than the particle size of Mg2Si. The Mg2Si particles cannot be effective flux pinning centers, but are rather useless impurities in the MgB2 matrix, which decrease the density of current carriers. However, the free C and Si can be very strong flux pinning centers because of their small sizes, which are responsible for the high *Jc* performance in high magnetic fields. According to the collective pinning model [113], the *Jc* performance in the low magnetic field region depends on the density of current carriers due to its weak field dependence, while the high magnetic field *Jc* performance depends on the flux pinning force due to the increased high *Hc*2 and *Hirr*. The approximate *Hsb* values are also indicated on the *Jc* curves estimated at 20 K, as shown in the inset of Figure 16, where *Hsb* is the crossover field from single-vortex to small-bundle pinning based on the collective pinning model. However, *Hsb* has not been detected at 5 K due to the relatively high supercurrents [103].

The strength of the pinning force can be reflected by the dependence of *Hc*2 and *Hirr* on the normalized temperature, as shown in Figure 17. Carbon substitution is one of the most effective methods to improve the *Hc*2 and *Hirr* because of the increased scattering by C doping, and the increased scattering can also contribute to decreased *Tc* and merging of the two gaps [144]. It should be noted that the *Hc*2 and *Hirr* for 750in, 850in, and 750inex have their highest values at low temperature, which means a strong flux pinning force. The poor *J*c is of these samples attributed to the lower density of current carriers. Both 1050in and 1050inex show the lowest *H*c2 and the lowest *H*irr among all the samples. 850in, 950in, 850inex, and 950inex show competitive *H*c2 and *H*irr performances, which are responsible for their high *J*c values under high magnetic field.

The *Jc* dependence on the applied field is shown in Figure 16 for typical samples, which were measured at 5 K and 20 K, respectively. It should be noted that the *Jc* dependence on sintering temperature in this work is totally different from previously reported results, because the solidliquid reaction dynamics is different due to the small SiC particle size, less than 15 nm, which is much smaller than the particle sizes used before. The *Jc* benefits from the high sintering temperature. 750in, 850in, and 750inex display non-competitive performance over the whole field range. 1050inex has very high low field *Jc* values but its *Jc* deteriorates with increasing magnetic field. The *Jc* properties of 950in, 850inex, and 950inex show outstandingly high *Jc* performances among all the samples. It is concluded that the *in-situ*/*ex-situ* combined technique only requires a lower sintering temperature to achieve high quality MgB2 wires, which is very important for industrial application in terms of energy saving and equipment simplification. The *Jc* values of 750inex are double those of 750in at 5 K and 20 K over the measured magnetic field range. The inset of Figure 16 displays the low field performances at 20 K to avoid the influence of the flux jumping effect. 750in and 750inex show quite low *Jc* values in lower magnetic field. 1050in and 850inex show competitive self-field *Jc*. The ball-milling process used to produce the *ex-situ* MgB2 powder destroyes the porous structure and enhances the density of MgB2 fabricated by the *in-situ*/*ex-situ* combined process. This is because of the small particle size of SiC used in this work, which induces different reaction dynamics during the *in-situ* or *in-situ*/*ex-situ* processing [81, 104, 141, 142], so that the present *Jc* dependence on sintering temperature is quite different from what has been previously reported. It is proposed that the liquid Mg reacts with SiC first to form Mg2Si and releases free C at low sintering temperature. Then the Mg2Si reacts with B to form MgB2 and releases free Si at high sintering temperatures. Both C and Si have very small sizes and cannot be detected by XRD. The coherence length, ξ, of MgB2 is anisotropic. *ξ*ab(0) = 3.7 – 12 nm, and *ξ*c(0) = 1.6 - 3.6 nm [110], which is shorter than the particle size of Mg2Si. The Mg2Si particles cannot be effective flux pinning centers, but are rather useless impurities in the MgB2 matrix, which decrease the density of current carriers. However, the free C and Si can be very strong flux pinning centers because of their small sizes, which are responsible for the high *Jc* performance in high magnetic fields. According to the collective pinning model [113], the *Jc* performance in the low magnetic field region depends on the density of current carriers due to its weak field dependence, while the high magnetic field *Jc* performance depends on the flux pinning force due to the increased high *Hc*2 and *Hirr*. The approximate *Hsb* values are also indicated on the *Jc* curves estimated at 20 K, as shown in the inset of Figure 16, where *Hsb* is the crossover field from single-vortex to small-bundle pinning based on the collective pinning model. However, *Hsb* has not been detected at 5 K due

The strength of the pinning force can be reflected by the dependence of *Hc*2 and *Hirr* on the normalized temperature, as shown in Figure 17. Carbon substitution is one of the most effective methods to improve the *Hc*2 and *Hirr* because of the increased scattering by C doping, and the increased scattering can also contribute to decreased *Tc* and merging of the two gaps [144]. It should be noted that the *Hc*2 and *Hirr* for 750in, 850in, and 750inex have their highest values at low temperature, which means a strong flux pinning force. The poor *J*c is of these samples attributed to the lower density of current carriers. Both 1050in and 1050inex show the lowest *H*c2 and the lowest *H*irr among all the samples. 850in, 950in, 850inex, and 950inex show competitive *H*c2 and *H*irr performances, which are responsible for their high *J*c values under

to the relatively high supercurrents [103].

112 Superconductors – New Developments

high magnetic field.

**Figure 16.** *Jc* at 5 K and 20 K. The inset indicates the *Jc* behavior in low magnetic field at 20 K. *Hsb*, the crossover field from single-vortex to small-bundle pinning, is indicated by the dashed-dotted line at its probable position on the *Jc* curves [140].

**Figure 17.** Comparison of *Hc2* (solid symbols) and *Hirr* (open symbols) for (a) MgB2/Fe wires doped with nano-SiC and (b) MgB2/Fe wires doped with nano-SiC, with sintering at 750, 850, 950, and 1050 o C, respectively [140].

In conclusion, high sintering temperature can improve the critical current density of smallparticle-size SiC doped MgB2. The two-step reactions between Mg, SiC, and B release free C and Si to form strong flux pinning centers. The current carrier density and flux pinning force are important factors in the improvement of the *J*<sup>c</sup> performance of nano-SiC doped MgB2. The current carrier density determines the *J*c behavior in the single-vortex regime, where *J*<sup>c</sup> is independent of applied magnetic field. The flux pinning force determines the *J*c performance in the small-bundle pinning regime, where the doping induced defects are believed to act as flux pinning centers. Nano-SiC doped MgB2/Fe wires fabricated by the combined process are worth ongoing research to develop optimized processing parameters for practical purposes.

#### **5. Conclusions**

The diffusion method can greatly improve the critical current density compared with the normal technique, which indicates that the critical current density greatly depends on the connectivity of MgB2 grains. The combined process improves the connectivity of MgB2 grains and the compactness of the superconducting core in wires, which induces high critical current density in zero field. The flux pinning force can also be improved by dopants for magnetic field application. Further research could focus on parameter optimization of the combined process to fabricate high quality MgB2 wires.

#### **Acknowledgements**

The authors thank Dr. T. Silver for her useful discussions. This work is supported by the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, the Australian Research Council (project ID: DP0770205), and Hyper Tech Research Inc.

#### **Author details**

Wenxian Li1,2,3\* and Shi-Xue Dou2

\*Address all correspondence to: shuliwx@shu.edu.cn

1 School of Materials Science & Engineering, Shanghai University, Shanghai, China

2 Institute for Superconducting & Electronic Materials, University of Wollongong, Wollongong, Australia

3 School of Computing, Engineering & Mathematics, University of Western Sydney, Sydney, Australia

#### **References**

In conclusion, high sintering temperature can improve the critical current density of smallparticle-size SiC doped MgB2. The two-step reactions between Mg, SiC, and B release free C and Si to form strong flux pinning centers. The current carrier density and flux pinning force are important factors in the improvement of the *J*<sup>c</sup> performance of nano-SiC doped MgB2. The current carrier density determines the *J*c behavior in the single-vortex regime, where *J*<sup>c</sup> is independent of applied magnetic field. The flux pinning force determines the *J*c performance in the small-bundle pinning regime, where the doping induced defects are believed to act as flux pinning centers. Nano-SiC doped MgB2/Fe wires fabricated by the combined process are worth ongoing research to develop optimized processing parameters for practical purposes.

The diffusion method can greatly improve the critical current density compared with the normal technique, which indicates that the critical current density greatly depends on the connectivity of MgB2 grains. The combined process improves the connectivity of MgB2 grains and the compactness of the superconducting core in wires, which induces high critical current density in zero field. The flux pinning force can also be improved by dopants for magnetic field application. Further research could focus on parameter optimization of the combined

The authors thank Dr. T. Silver for her useful discussions. This work is supported by the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, the Australian Research Council (project ID: DP0770205), and Hyper Tech

1 School of Materials Science & Engineering, Shanghai University, Shanghai, China

2 Institute for Superconducting & Electronic Materials, University of Wollongong,

3 School of Computing, Engineering & Mathematics, University of Western Sydney, Sydney,

**5. Conclusions**

114 Superconductors – New Developments

**Acknowledgements**

Research Inc.

**Author details**

Wollongong, Australia

Australia

Wenxian Li1,2,3\* and Shi-Xue Dou2

\*Address all correspondence to: shuliwx@shu.edu.cn

process to fabricate high quality MgB2 wires.


[27] Rowell JM, Xu SY, Zeng H, Pogrebnyakov AV, Li Q, Xi XX, Redwing JM, Tian W, and Pan XQ, Critical current density and resistivity of MgB2 films, Appl. Phys. Lett. 2003; 83(1) 102-104.

[14] Dou SX, Shcherbakova O, Yeoh WK, Kim JH, Soltanian S, Wang XL, Senatore C, Flu‐ kiger R, Dhalle M, Husnjak O, and Babic E, Mechanism of enhancement in electro‐ magnetic properties of MgB2 by nano SiC doping, Phys. Rev. Lett. 2007; 98(9) 097002.

[15] Tinkham M, Introduction to Superconductivity, 2nd ed., New York: McGraw-Hill,,

[16] Nicol EJ and Carbotte JP, Theory of the critical current in two-band superconductors

[17] Arcos DH and Kunchur MN, Suppressed flux motion in magnesium diboride films,

[18] Eisterer M, Magnetic properties and critical currents of MgB2, Supercond. Sci. Tech‐

[19] Finnemore DK, Ostenson JE, Bud'ko SL, Lapertot G, and Canfield PC, Thermody‐ namic and transport properties of superconducting Mg10B2, Phys. Rev. Lett. 2001;

[20] Kawano K, Abell JS, Kambara M, Babu NH, and Cardwell DA, Evidence for high in‐ tergranular current flow in a single-phase polycrystalline MgB2 superconductor,

[21] Rowell JM, The widely variable resistivity of MgB2 samples, Supercond. Sci. Technol.

[22] Klie RF, Idrobo JC, Browning ND, Regan KA, Rogado NS, and Cava RJ, Direct obser‐ vation of nanometer-scale Mg- and B-oxide phases at grain boundaries in MgB2,

[23] Pogrebnyakov AV, Xi XX, Redwing JM, Vaithyanathan V, Schlom DG, Soukiassian A, Mi SB, Jia CL, Giencke JE, Eom CB, Chen J, Hu YF, Cui Y, and Li Q, Properties of

[24] Hassler W, Birajdar B, Gruner W, Herrmann M, Perner O, Rodig C, Schubert M, Hol‐ zapfel B, Eibl O, and Schultz L, MgB2 bulk and tapes prepared by mechanical alloy‐ ing: influence of the boron precursor powder, Supercond. Sci. Technol. 2006; 19(6)

[25] Fischer C, Hassler W, Rodig C, Perner O, Behr G, Schubert M, Nenkov K, Eckert J, Holzapfel B, and Schultz L, Critical current densities of superconducting MgB2 tapes prepared on the base of mechanically alloyed precursors, Physica C 2004; 406(1-2)

[26] Yeoh WK, Kim JH, Horvat J, Dou SX, and Munroe P, Improving flux pinning of MgB2 by carbon nanotube doping and ultrasonication, Supercond. Sci. Technol. 2006;

MgB2 thin films with carbon doping, Appl. Phys. Lett. 2004; 85(11) 2017-2019.

with application to MgB2, Phys. Rev. B 2005; 72(1) 014520.

Phys. Rev. B 2005; 71(18) 184516.

Appl. Phys. Lett. 2001; 79(14) 2216-2218.

Appl. Phys. Lett. 2001; 79(12) 1837-1839.

nol. 2007; 20(12) R47-R73.

86(11) 2420-2422.

2003; 16(6) R17-R27.

512-520.

121-130.

19(2) L5-L8.

1996; 123.

116 Superconductors – New Developments


[51] Shcherbakova O, Dou SX, Soltanian S, Wexler D, Bhatia M, Sumption M, and Col‐ lings EW, The effect of doping level and sintering temperature on *J*c(*H*) performance in nano-SiC doped and pure MgB2 wires, J. Appl. Phys. 2006; 99(8) 08M510.

[39] Yamada H, Hirakawa M, Kumakura H, and Kitaguchi H, Effect of aromatic hydro‐ carbon addition on *in situ* powder-in-tube processed MgB2 tapes, Supercond. Sci.

[40] Goldacker W, Schlachter SI, Obst B, Liu B, Reiner J, and Zimmer S, Development and performance of thin steel reinforced MgB2 wires and low-temperature processing for

[41] Matsumoto A, Kumakura H, Kitaguchi H, Senkowicz BJ, Jewell MC, Hellstrom EE, Zhu Y, Voyles PM, and Larbalestier DC, Evaluation of connectivity, flux pinning, and upper critical field contributions to the critical current density of bulk pure and

[42] Yamamoto A, Shimoyama J, Ueda S, Iwayama I, Horii S, and Kishio K, Effects of B4C doping on critical current properties of MgB2 superconductor, Supercond. Sci. Tech‐

[43] Perner O, Habler W, Eckert R, Fischer C, Mickel C, Fuchs G, Holzapfel B, and Schultz L, Effects of oxide particle addition on superconductivity in nanocrystalline MgB2

[44] Jiang CH, Nakane T, and Kumakura H, Superior high-field current density in slight‐

[45] Wu YF, Lu YF, Yan G, Li JS, Feng Y, Tang HP, Chen SK, Xu HL, Li CS, and Zhang PX, Improved superconducting properties in bulk MgB2 prepared by high-energy milling of Mg and B powders, Supercond. Sci. Technol. 2006; 19(11) 1215-1218. [46] Kim JH, Yeoh WK, Qin MJ, Xu X, and Dou SX, The doping effect of multiwall carbon nanotube on MgB2/Fe superconductor wire, J. Appl. Phys. 2006; 100(1) 013908. [47] Kim JH, Zhou S, Hossain MSA, Pan AV, and Dou SX, Carbohydrate doping to en‐ hance electromagnetic properties of MgB2 superconductors, Appl. Phys. Lett. 2006;

[48] Chen SK, Lockman Z, Wei M, Glowacki BA, and MacManus-Driscoll JL, Improved current densities in MgB2 by liquid-assisted sintering, Appl. Phys. Lett. 2005; 86(24)

[49] Ueda S, Shimoyama J, Iwayama I, Yamamoto A, Katsura Y, Horii S, and Kishio K, High critical current properties of MgB2 bulks prepared by a diffusion method, Appl.

[50] Zhang XP, Gao ZS, Wang DL, Yu ZG, Ma YW, Awaji S, and Watanabe K, Improved critical current densities in MgB2 tapes with ZrB2 doping, Appl. Phys. Lett. 2006;

ly Mg-deficient MgB2 tapes, Appl. Phys. Lett. 2005; 87(25) 252505.

further improvements, Supercond. Sci. Technol. 2004; 17(5) S363-S368.

SiC-alloyed MgB2, Appl. Phys. Lett. 2006; 89(13) 132508.

bulk samples, Physica C 2005; 432(1-2) 15-24.

Technol. 2006; 19(2) 175-177.

118 Superconductors – New Developments

nol. 2005; 18(10) 1323-1328.

89(14) 142505.

89(13) 132510.

Phys. Lett. 2005; 86(22) 222502.

242501.


[77] Kovac P, Husek I, Skakalova V, Meyer J, Dobrocka E, Hirscher M, and Roth S, Trans‐ port current improvements of *in situ* MgB2 tapes by the addition of carbon nano‐ tubes, silicon carbide or graphite, Supercond. Sci. Technol. 2007; 20(1) 105-111.

[64] Grovenor CRM, Goodsir L, Salter CJ, Kovac P, and Husek I, Interfacial reactions and oxygen distribution in MgB2 wires in Fe, stainless steel and Nb sheaths, Supercond.

[65] Senkowicz BJ, Giencke JE, Patnaik S, Eom CB, Hellstrom EE, and Larbalestier DC, Improved upper critical field in bulk-form magnesium diboride by mechanical alloy‐

[66] Dou SX, Shcherbakova O, Yoeh WK, Kim JH, Soltanian S, Wang XL, Senatore C, Flu‐ kiger R, Dhalle M, Husnjak O, and Babic E, Mechanism of enhancement in electro‐ magnetic properties of MgB2 by nano SiC doping, Phys. Rev. Lett. 2007; 98(9) 097002.

[67] Zhao Y, Feng Y, Shen TM, Li G, Yang Y, and Cheng CH, Cooperative doping effects of Ti and C on critical current density and irreversibility field of MgB2, J. Appl. Phys.

[68] Xu X, Kim JH, Yeoh WK, Zhang Y, and Dou SX, Improved *J*c of MgB2 superconductor by ball milling using different media, Supercond. Sci. Technol. 2006; 19(11) L47-L50.

[69] Haigh S, Kovac P, Prikhna TA, Savchuk YM, Kilburn MR, Salter C, Hutchison J, and Grovenor C, Chemical interactions in Ti doped MgB2 superconducting bulk samples

[70] Ma YW, Kumakura H, Matsumoto A, Hatakeyama H, and Togano K, Improvement of critical current density in Fe-sheathed MgB2 tapes by ZrSi2, ZrB2 and WSi2 doping,

[71] Kumar D, Pennycook SJ, Narayan J, Wang H, and Tiwari A, Role of silver addition in the synthesis of high critical current density MgB2 bulk superconductors, Supercond.

[72] Yamamoto A, Shimoyama J, Ueda S, Katsura Y, Iwayama I, Horii S, and Kishio K, Universal relationship between crystallinity and irreversibility field of MgB2, Appl.

[73] Lezza P, Senatore C, and Flukiger R, Improved critical current densities in B4C doped

[74] Yeoh WK, Kim JH, Horvat J, Xu X, Qin MJ, Dou SX, Jiang CH, Nakane T, Kumakura H, and Munroe P, Control of nano carbon substitution for enhancing the critical cur‐

[75] Dou SX, Yeoh WK, Horvat J, and Ionescu M, Effect of carbon nanotube doping on critical current density of MgB2 superconductor, Appl. Phys. Lett. 2003; 83(24)

[76] Kim JH, Yeoh WK, Qin MJ, Xu X, Dou SX, Munroe P, Kumakura H, Nakane T, and Jiang CH, Enhancement of in-field *J*c in MgB2/Fe wire using single- and multiwalled

MgB2 based wires, Supercond. Sci. Technol. 2006; 19(10) 1030-1033.

rent density in MgB2, Supercond. Sci. Technol. 2006; 19(6) 596-599.

carbon nanotubes, Appl. Phys. Lett. 2006; 89(12) 122510.

Sci. Technol. 2004; 17(3) 479-484.

120 Superconductors – New Developments

2006; 100(12) 123902.

ing with carbon, Appl. Phys. Lett. 2005; 86(20) 202502.

and wires, Supercond. Sci. Technol. 2005; 18(9) 1190-1196.

Supercond. Sci. Technol. 2003; 16(8) 852-856.

Sci. Technol. 2003; 16(4) 455-458.

Phys. Lett. 2005; 86(21) 212502.

4996-4998.


[101] Suo HL, Beneduce C, Dhalle M, Musolino N, Genoud JY, and Flukiger R, Large transport critical currents in dense Fe- and Ni-clad MgB2 superconducting tapes, Appl. Phys. Lett. 2001; 79(19) 3116-3118.

[89] Sumption MD, Bhatia M, Rindfleisch M, Tomsic M, Soltanian S, Dou SX, and Col‐ lings EW, Large upper critical field and irreversibility field in MgB2 wires with SiC

[90] Hossain MSA, Kim JH, Wang XL, Xu X, Peleckis G, and Dou SX, Enhancement of flux pinning in a MgB2 superconductor doped with tartaric acid, Supercond. Sci.

[91] Liao XZ, Serquis A, Zhu YT, Civale L, Hammon DL, Peterson DE, Mueller FM, Nes‐ terenko VF, and Gu Y, Defect structures in MgB2 wires introduced by hot isostatic

[92] Gao ZS, Ma YW, Zhang XP, Wang DL, Yu ZG, Watanabe K, Yang HA, and Wen HH, Strongly enhanced critical current density in MgB2/Fe tapes by stearic acid and stea‐

[93] Wen HH, Li SL, Zhao ZW, Jin H, Ni YM, Ren ZA, Che GC, and Zhao ZX, Magnetic relaxation and critical current density of the new superconductor MgB2, Supercond.

[94] Prikhna TA, Gawalek W, Savchuk YM, Moshchil VE, Sergienko NV, Habisreuther T, Wendt M, Hergt R, Schmidt C, Dellith J, Melnikov VS, Assmann A, Litzkendorf D, and Nagorny PA, High-pressure synthesis of MgB2 with addition of Ti, Physica C

[95] Serquis A, Liao XZ, Zhu YT, Coulter JY, Huang JY, Willis JO, Peterson DE, Mueller FM, Moreno NO, Thompson JD, Nesterenko VF, and Indrakanti SS, Influence of mi‐ crostructures and crystalline defects on the superconductivity of MgB2, J. Appl. Phys.

[96] Serquis A, Civale L, Hammon DL, Liao XZ, Coulter JY, Zhu YT, Jaime M, Peterson DE, Mueller FM, Nesterenko VF, and Gu Y, Hot isostatic pressing of powder in tube

[97] Eyidi D, Eibl O, Wenzel T, Nickel KG, Schlachter SI, and Goldacker W, Supercon‐ ducting properties, microstructure and chemical composition of MgB2 sheathed ma‐

[98] Pan AV, Zhou SH, Liu HK, and Don SX, Properties of superconducting MgB2 wires:

[99] Serquis A, Civale L, Hammon DL, Coulter JY, Liao XZ, Zhu YT, Peterson DE, and Mueller FM, Microstructure and high critical current of powder-in-tube MgB2, Appl.

[100] Serquis A, Civale L, Hammon DL, Liao XZ, Coulter JY, Zhu YT, Peterson DE, and Mueller FM, Role of excess Mg and heat treatments on microstructure and critical

versus reaction technique, Supercond. Sci. Technol. 2003; 16(5) 639-644.

additions, Appl. Phys. Lett. 2005; 86(9) 092507.

pressing, Supercond. Sci. Technol. 2003; 16(7) 799-803.

rate doping, Supercond. Sci. Technol. 2007; 20(5) 485-489.

MgB2 wires, Appl. Phys. Lett. 2003; 82(17) 2847-2849.

terials, Supercond. Sci. Technol. 2003; 16(7) 778-788.

current of MgB2 wires, J. Appl. Phys. 2003; 94(6) 4024-4031.

Phys. Lett. 2003; 82(11) 1754-1756.

Technol. 2007; 20(1) 112-116.

122 Superconductors – New Developments

Sci. Technol. 2002; 15(3) 315-319.

2004; 402(3) 223-233.

2002; 92(1) 351-356.


[128] Li WX, Li Y, Zhu MY, Chen RH, Xu X, Yeoh WK, Kim JH, and Dou SX, Benzoic acid doping to enhance electromagnetic properties of MgB2 superconductors, IEEE Trans. Appl. Supercond. 2007; 17(2) 2778-2781.

[114] Li WX, Li Y, Chen RH, Zeng R, Zhu MY, Jin HM, and Dou SX, Electron-phonon cou‐ pling properties in MgB2 observed by Raman scattering, J. Phys.-Condens. Matter

[115] Li WX, Li Y, Chen RH, Zeng R, Dou SX, Zhu MY, and Jin HM, Raman study of ele‐ ment doping effects on the superconductivity of MgB2, Phys. Rev. B 2008; 77(9)

[116] Li WX, Zeng R, Poh CK, Li Y, and Dou SX, Magnetic scattering effects in two-band superconductor: the ferromagnetic dopants in MgB2, J. Phys.-Condens. Matter 2010;

[117] Shi L, Zhang HR, Chen L, and Feng Y, The Raman spectrum and lattice parameters of MgB2 as a function of temperature, J. Phys.-Condens. Matter 2004; 16(36)

[118] Allen PB, Neutron spectroscopy of superconductors, Phys. Rev. B 1972; 6(7)

[119] Kortus J, Dolgov OV, Kremer RK, and Golubov AA, Band filling and interband scat‐ tering effects in MgB2: Carbon versus aluminum doping, Phys. Rev. Lett. 2005; 94(2)

[120] McMillan WL, Transition temperature of strong-coupled superconductors, Phys.

[121] Allen PB and Dynes RC, Transition-temperature of strong-coupled superconductors

[122] Kortus J, Mazin II, Belashchenko KD, Antropov VP, and Boyer LL, Superconductivi‐

[123] Osborn R, Goremychkin EA, Kolesnikov AI, and Hinks DG, Phonon density of states

[124] Brinkman A, Golubov AA, Rogalla H, Dolgov OV, Kortus J, Kong Y, Jepsen O, and Andersen OK, Multiband model for tunneling in MgB2 junctions, Phys. Rev. B 2002;

[125] Collings EW, Sumption MD, Bhatia M, Susner MA, and Bohnenstiehl SD, Prospects for improving the intrinsic and extrinsic properties of magnesium diboride supercon‐

[126] Li WX, Li Y, Chen RH, Yeoh WK, and Dou SX, Effect of magnetic field processing on the microstructure of carbon nanotubes doped MgB2, Physica C 2007; 4601)570-571.

[127] Yeoh WK, Horvat J, Dou SX, and Munroe P, Effect of carbon nanotube size on super‐ conductivity properties of MgB2, IEEE Trans. Appl. Supercond. 2005; 15(2) 3284-3287.

ty of metallic boron in MgB2, Phys. Rev. Lett. 2001; 86(20) 4656-4659.

ducting strands, Supercond. Sci. Technol. 2008; 21(10) 103001.

2008; 20(25) 255235.

094517.

124 Superconductors – New Developments

22(13) 135701.

6541-6550.

2577-2579.

027002.

65(18) 180517.

Rev. 1968; 167(2) 331-334.

reanalyzed, Phys. Rev. B 1975; 12(3) 905-922.

in MgB2, Phys. Rev. Lett. 2001; 87(1) 017005.

