**1.1 The phase formation mechanism of MgB2 during sintering**

The superconductivity at 39 K discovered in MgB2 among simple binary chemical composition attracted much interest in its fabrication techniques and practical applications [1]. MgB2 superconductor exhibits many impressive properties such as highest critical temperature amongst intermetallic superconductors which means low cooling costs, impressive grain boundary transparency to the flow of current which leads to greater critical current density [2- 4], comparatively large coherence length which allows a better Josephson junction fabrication, low material cost which will lead to a cheaper superconductor technology, simple crystal structure, etc. Hence, MgB2 superconductors, especially the MgB2 wires and coils, have the outstanding potential to be integrated into diverse commercial applications, such as, magnetic resonance imaging (MRI) [5, 6] , fault current limiters (FCL), Josephson junctions and SQUID [7, 8, 9], transformers, motors, generators, adiabatic demagnetization refrigerators, magnetic separators, magnetic levitation applications, energy storage, and high energy physical applications. But the MgB2 itself is mechanically hard and brittle and therefore not amenable to drawing into the desired wire and tape geometry. Thus, the powder-in-tube (PIT) technique that was used to make the Y-Ba-Cu-O oxide superconductor has been employed in the fabrication of MgB2 wires and tapes these years [10-14]. So far, in-situ sintering, including the in-situ PIT, from the mixture of magnesium and boron is the major method to fabricate MgB2 superconductors (bulks, wires and tapes). The corresponding sintering parameters have a significant influence on the superconducting properties of MgB2. Thus it is necessary to investigate the sintering mechanism of MgB2 superconductors.

The reaction process and MgB2 phase formation mechanism during the sintering have been studied by different methods, such as differential thermal analysis (DTA) [15-21], *in-situ* XRD measurement [22-25], *in-situ* resistance measurement [26, 27] and temperature dependent magnetization (M–T) measurements [28].

#### **1.2 Sintering of Mg-B precursor powders over a wide temperature range**

It can be seen from the DTA data of the Mg + 2Bamorphous precursor composition shown in Fig. 1 that the first exothermic peak occurs in the temperature range below 650 oC (the

Sintering Process and Its Mechanism of MgB2 Superconductors 471

Fig. 2. The in-situ XRD patterns of (a) Cu-doped MgB2 sample and (b) undoped MgB2

**1.3 Sintering process and mechanism of MgB2 superconductors at high temperature**  Since most of MgB2 superconductors are prepared by sintering at high temperature, it makes sense to investigate their phase formation process and sintering mechanism at high sintering temperature. At high temperature, the liquid-solid reaction between Mg and B is activated following completion of the melting of Mg. The MgB2 phase formation mechanism at this stage should be very different to that at the solid-solid reaction stage due to the

A large number of small MgB2 grains exist in the bulk material after the solid-solid reaction, together with residual Mg and B particles. When the sintering temperature is above 650 oC, residual Mg melted and the flowing liquid phase (Mg) increased the diffusion rate of atom and enlarged the contact area of reactants, which leads to a strong and complete reaction

According to our previous study [17], this solid-liquid reaction stage follows Ostwald

i. *rearrangement of particles*. The molten Mg helps individual particles to slip, spin and

ii. *solid-liquid reaction*. The residual B particles are entrapped by the molten Mg, which

iii. *solution-reprecipitation and grain growth*. Small MgB2 grains generally have a higher solubility in the liquid phase than larger grains [33] and will dissolve first in the Mg melt to yield an over-saturated solution. This will lead to the precipitation of MgB2 on the surface of existing MgB2 grains, which will lead to further grain growth, as shown

ripening mechanism and includes three important processes [32]:

promotes a strong instantaneous contact reaction;

sample.

presence of the Mg melt.

between residual Mg and B.

reassemble;

in Fig. 3.

melting point of Mg) for samples heated at either 20 oC /min or 5 oC /min [29]. Previous studies have suggested different origins of this peak; some speculate that it is due to the reaction between Mg and impurity B2O3 in the original B powder [30, 31], whereas others suggest that it is associated with the solid-solid reaction between Mg and B [16, 18]. In general, there is consensus about the origin of the second and third DTA peaks, which are due to melting of Mg and the liquid-solid reaction between and B, respectively.

Fig. 1. The measured thermal analysis curves during the sintering of Mg + 2B sample with heating rates of 20 oC⋅min-1 and 5 oC⋅min-1[29].

With aim of clarifying the origin of first exothermic peak in the DTA curves, the phase evolution of Mg + 2Bamorphous system was detected by in-situ X-ray diffractometer (XRD) during the sintering up to 750 oC and the measured results are shown in Fig. 2. It is found that obvious MgB2 phase peaks can be recognized only after 550 oC. In fact, all the measured results of in-situ resistance, *in-situ* XRD and the temperature dependent magnetization during sintering of a mixed powder of Mg : B = 1 : 2 indicate that the MgB2 phase begins to form before the Mg melting [22, 24, 25, 27, 28]. In this case, the exothermic peak in the DTA curves before the Mg melting occurs, and should be attributed to the solid-solid reaction between Mg and B. The phase formation of MgB2 during the sintering process, therefore, proceeds via solid-solid reaction, Mg melting and, finally, liquid-solid reaction.

Observing the in-situ XRD patterns in Fig. 2 carefully, a lot of Mg is still present as primary phase in the Mg+2B sample sintered at 600 oC. The result implies that the MgB2 phase formed at the solid-solid reaction stage is limited due to the low atomic diffusion rate in the solid state. On the other hand, also as shown in Fig. 2, MgB2 phase forms on a much larger scale and becomes primary phase immediately following completion of the melting of Mg when the sintering temperature reaches 650 oC. As a result, in order to obtain complete MgB2 phase rapidly, the MgB2 superconductors were generally synthesized by sintering at high temperature in the past decade.

melting point of Mg) for samples heated at either 20 oC /min or 5 oC /min [29]. Previous studies have suggested different origins of this peak; some speculate that it is due to the reaction between Mg and impurity B2O3 in the original B powder [30, 31], whereas others suggest that it is associated with the solid-solid reaction between Mg and B [16, 18]. In general, there is consensus about the origin of the second and third DTA peaks, which are

Fig. 1. The measured thermal analysis curves during the sintering of Mg + 2B sample with

With aim of clarifying the origin of first exothermic peak in the DTA curves, the phase evolution of Mg + 2Bamorphous system was detected by in-situ X-ray diffractometer (XRD) during the sintering up to 750 oC and the measured results are shown in Fig. 2. It is found that obvious MgB2 phase peaks can be recognized only after 550 oC. In fact, all the measured results of in-situ resistance, *in-situ* XRD and the temperature dependent magnetization during sintering of a mixed powder of Mg : B = 1 : 2 indicate that the MgB2 phase begins to form before the Mg melting [22, 24, 25, 27, 28]. In this case, the exothermic peak in the DTA curves before the Mg melting occurs, and should be attributed to the solid-solid reaction between Mg and B. The phase formation of MgB2 during the sintering process, therefore,

Observing the in-situ XRD patterns in Fig. 2 carefully, a lot of Mg is still present as primary phase in the Mg+2B sample sintered at 600 oC. The result implies that the MgB2 phase formed at the solid-solid reaction stage is limited due to the low atomic diffusion rate in the solid state. On the other hand, also as shown in Fig. 2, MgB2 phase forms on a much larger scale and becomes primary phase immediately following completion of the melting of Mg when the sintering temperature reaches 650 oC. As a result, in order to obtain complete MgB2 phase rapidly, the MgB2 superconductors were generally synthesized by sintering at

proceeds via solid-solid reaction, Mg melting and, finally, liquid-solid reaction.

heating rates of 20 oC⋅min-1 and 5 oC⋅min-1[29].

high temperature in the past decade.

due to melting of Mg and the liquid-solid reaction between and B, respectively.

Fig. 2. The in-situ XRD patterns of (a) Cu-doped MgB2 sample and (b) undoped MgB2 sample.

#### **1.3 Sintering process and mechanism of MgB2 superconductors at high temperature**

Since most of MgB2 superconductors are prepared by sintering at high temperature, it makes sense to investigate their phase formation process and sintering mechanism at high sintering temperature. At high temperature, the liquid-solid reaction between Mg and B is activated following completion of the melting of Mg. The MgB2 phase formation mechanism at this stage should be very different to that at the solid-solid reaction stage due to the presence of the Mg melt.

A large number of small MgB2 grains exist in the bulk material after the solid-solid reaction, together with residual Mg and B particles. When the sintering temperature is above 650 oC, residual Mg melted and the flowing liquid phase (Mg) increased the diffusion rate of atom and enlarged the contact area of reactants, which leads to a strong and complete reaction between residual Mg and B.

According to our previous study [17], this solid-liquid reaction stage follows Ostwald ripening mechanism and includes three important processes [32]:


Sintering Process and Its Mechanism of MgB2 Superconductors 473

As discussed above, the formation of the MgB2 phase begins at a temperature below the melting point of Mg, which offers the prospect of sintering MgB2 superconductors at relatively low temperature (i.e. below the melting point of Mg) in an attempt to avoid problems associated with the strong volatility and oxidation of Mg at high temperature. Rogado *et al.* [34] initially fabricated superconducting bulk MgB2 samples by conventional solid state sintering at a temperature as low as 550 °C (see Fig. 5). This process required a sintering time of 16 hours to form the complete bulk MgB2 phase, and the samples exhibited inferior superconducting properties than those sintered at high temperature. However, the result indicates that it is possible to fabricate MgB2 superconductors at low temperature and this work resulted in increased attempts world-wide to develop a low-temperature sintering

Yamamoto *et al.* [35] found that MgB2 bulk superconductors prepared by solid state sintering at 600°C for 240 h exhibited improved critical current densities at 20 K (see Fig. 11). This study confirmed the potential of the low temperature sintering technique for the fabrication of bulk MgB2 superconductors. It also established that poor crystallinity is found to enhance *H*c2, *H*irr and *J*c in MgB2 at high fields, whereas strong grain connectivity, reduced

MgB2 wires and tapes with improved *H*irr and *J*c can also be prepared by low temperature sintering by an *in-situ* PIT technique. Goldacker *et al.* [36] reports the synthesis of thin, steelreinforced MgB2 wires with very high transport current densities at only 640 °C. These authors suggest that the low-temperature annealing could lead to a fine grain structure and a superconducting percolation path with very high associated critical current density. Moreover, the observation of a dramatically-reduced reaction layer between the filament and sheath in their samples is very promising for the production of filaments with small

MgO impurity content and a smaller grain size increases *J*c at low fields.

process for both undoped and doped MgB2 bulk superconductors.

Fig. 4. SEM image of MgB2 sample sintered at 750 oC.

diameters in mono- and multifilamentary wire.

Fig. 3. Schematic illustration of the solution-reprecipitiation and growth process of grains during the liquid-solid stage [17].

According to above discussion, when the sintering temperature rise to 750 oC, the ending point of solid-liquid reaction in the DTA curve (see Fig. 1), complete MgB2 phase can be obtained (see Fig. 2) and most of MgB2 grains tend to be regular hexagon in the sample (see Fig. 4, the SEM image of sample sintered at 750 oC).

It is very difficult to calculate the kinetic parameters exactly from the DTA analysis data due to the overlap between the Mg melting and liquid-solid reaction thermal peaks. Hence, only limited kinetic information calculated from the *in-situ* X-ray diffraction measurement has been reported for the liquid-solid reaction between Mg and B. DeFouw *et al.* Ref. [23] reports that the liquid-solid reaction between Mg and B under isothermal conditions can be described by diffusion-controlled models of a reacting sphere with kinetics characterized by diffusion coefficients that increase with temperature from 2 × 1017 to 3 × 1016 s-1, with associated activation energies of 123 ~ 143 kJ⋅mol-1. However, a very high heating rate was used in these studies to prevent the reaction between Mg and B occurring below a certain temperature (above the melting point of Mg). As a result, the sintering environment might be quite different from that in traditional sintering methods.

Previous studies on the phase formation mechanism of MgB2 during liquid-solid sintering between Mg and B are deficient, and further investigation is necessary in addition to advanced test methods.

#### **1.4 Conventional solid-state sintering of MgB2 superconductors at low temperature**

Though high-temperature sintering is the most popular method of synthesizing MgB2 superconductors till now, the high volatility and tendency of Mg to oxidize at high temperature pose significant challenges to the fabrication of MgB2 superconductors that exhibit excellent superconductive properties since these processes tend to generate voids and MgO impurities during in-situ sintering. Thus, recent studies have addressed the lowtemperature preparation of MgB2 superconductors in an attempt to reduce the oxidation and volatility of Mg.

Fig. 3. Schematic illustration of the solution-reprecipitiation and growth process of grains

According to above discussion, when the sintering temperature rise to 750 oC, the ending point of solid-liquid reaction in the DTA curve (see Fig. 1), complete MgB2 phase can be obtained (see Fig. 2) and most of MgB2 grains tend to be regular hexagon in the sample (see

It is very difficult to calculate the kinetic parameters exactly from the DTA analysis data due to the overlap between the Mg melting and liquid-solid reaction thermal peaks. Hence, only limited kinetic information calculated from the *in-situ* X-ray diffraction measurement has been reported for the liquid-solid reaction between Mg and B. DeFouw *et al.* Ref. [23] reports that the liquid-solid reaction between Mg and B under isothermal conditions can be described by diffusion-controlled models of a reacting sphere with kinetics characterized by diffusion coefficients that increase with temperature from 2 × 1017 to 3 × 1016 s-1, with associated activation energies of 123 ~ 143 kJ⋅mol-1. However, a very high heating rate was used in these studies to prevent the reaction between Mg and B occurring below a certain temperature (above the melting point of Mg). As a result, the sintering environment might

Previous studies on the phase formation mechanism of MgB2 during liquid-solid sintering between Mg and B are deficient, and further investigation is necessary in addition to

**1.4 Conventional solid-state sintering of MgB2 superconductors at low temperature**  Though high-temperature sintering is the most popular method of synthesizing MgB2 superconductors till now, the high volatility and tendency of Mg to oxidize at high temperature pose significant challenges to the fabrication of MgB2 superconductors that exhibit excellent superconductive properties since these processes tend to generate voids and MgO impurities during in-situ sintering. Thus, recent studies have addressed the lowtemperature preparation of MgB2 superconductors in an attempt to reduce the oxidation

during the liquid-solid stage [17].

advanced test methods.

and volatility of Mg.

Fig. 4, the SEM image of sample sintered at 750 oC).

be quite different from that in traditional sintering methods.

As discussed above, the formation of the MgB2 phase begins at a temperature below the melting point of Mg, which offers the prospect of sintering MgB2 superconductors at relatively low temperature (i.e. below the melting point of Mg) in an attempt to avoid problems associated with the strong volatility and oxidation of Mg at high temperature. Rogado *et al.* [34] initially fabricated superconducting bulk MgB2 samples by conventional solid state sintering at a temperature as low as 550 °C (see Fig. 5). This process required a sintering time of 16 hours to form the complete bulk MgB2 phase, and the samples exhibited inferior superconducting properties than those sintered at high temperature. However, the result indicates that it is possible to fabricate MgB2 superconductors at low temperature and this work resulted in increased attempts world-wide to develop a low-temperature sintering process for both undoped and doped MgB2 bulk superconductors.

Fig. 4. SEM image of MgB2 sample sintered at 750 oC.

Yamamoto *et al.* [35] found that MgB2 bulk superconductors prepared by solid state sintering at 600°C for 240 h exhibited improved critical current densities at 20 K (see Fig. 11). This study confirmed the potential of the low temperature sintering technique for the fabrication of bulk MgB2 superconductors. It also established that poor crystallinity is found to enhance *H*c2, *H*irr and *J*c in MgB2 at high fields, whereas strong grain connectivity, reduced MgO impurity content and a smaller grain size increases *J*c at low fields.

MgB2 wires and tapes with improved *H*irr and *J*c can also be prepared by low temperature sintering by an *in-situ* PIT technique. Goldacker *et al.* [36] reports the synthesis of thin, steelreinforced MgB2 wires with very high transport current densities at only 640 °C. These authors suggest that the low-temperature annealing could lead to a fine grain structure and a superconducting percolation path with very high associated critical current density. Moreover, the observation of a dramatically-reduced reaction layer between the filament and sheath in their samples is very promising for the production of filaments with small diameters in mono- and multifilamentary wire.

Sintering Process and Its Mechanism of MgB2 Superconductors 475

Analysis of the kinetics of the sintering process can be performed based on the DTA data using different computational methods. Yan *et al.* [18] calculated the activation energy of the solid-solid reaction at low sintering temperature using the Ozawa–Flynn–Wall and Kissinger as 58.2 and 72.8 kJ⋅mol-1, respectively. The value of the pre-exponential factor calculated using the Kissinger method is 2.0 × 1015 s−1. They also report that the activation energy increases parabolic as the reaction progresses [18]. However, the study by Shi *et al.* [19] draws different conclusions to those of Yan et al. These authors use a new kinetic analysis (based on a variant on the Flynn-Wall-Ozawa method) under non-isothermal conditions and suggest that the solid-solid reaction between Mg and B powders follows an instantaneous nuclei growth (Avrami–Erofeev equation, *n* = 2) mechanism. The values of *E* 

**1.5 Sintering kinetics of MgB2 superconductors at low temperature** 

decrease from 175.4 to 160.4 kJ·mol-1 with the increase of the conversion degrees (

the low-temperature sintering combined with advanced test methods.

formation during the low-temperature sintering is carried out.

as the conversion degree reaches 0.9.

the External Standard Method.

oC and 600 oC (the XRD patterns in not shown here).

to 0.8 in this model. However, the activation energy (*E*) increases to 222.7 kJ·mol-1 [19] again

On the other hand, the solid-solid reaction between Mg and B exothermal peak is partly overlapped with the Mg melting endothermic peak in the DTA curves. This phenomenon makes it difficult to calculate the kinetics parameters exactly from the thermal analysis data and also could be the reason why the previous results are different from different research groups. It is necessary to further investigate the phase formation mechanism of MgB2 during

In our recent work [38], in-situ X-ray diffraction technique is used to measure the degree of reaction between Mg and B as a function of time at several certain temperatures below Mg melting, respectively. Based on these isothermal data, the kinetics analysis of MgB2 phase

Bulk samples of MgB2 were prepared by a solid-state sintering method using amorphous boron powder (99% purity, 25μm in size), magnesium powder (99.5% purity, 100 μm in size). Several reaction temperatures in the range of 550~600 oC, below the melting point of Mg, were chosen as the isothermal holding temperatures. Then the samples were fast-heated to the chosen temperature with a rate of 50 oC/min in order to prevent significant reaction between Mg and B before arriving at the isothermal annealing temperature. The x-ray diffraction measurement started as soon as the sample temperature reached the certain isothermal temperature and it will detect the sample every 15 min till the reaction is over. The weight fraction of synthesized MgB2 which corresponds to the degree of reaction was calculated from the XRD data of sample obtained after different soaking time according to

Fig. 6 illustrates the typical X-ray diffraction patterns of the Mg-B sample isothermally annealed at 575 oC for different periods. One can see that no organized MgB2 peak can be observed when the temperature just reaches 575 oC. It implies that the reaction between Mg and B did not occur during the rapid heating to the final isothermal holding temperature. As the holding time prolonging, the MgB2 phase appears and increases gradually while the Mg phase decreases. However, the increase in the intensity of MgB2 peaks becomes very slow and even stops when it reaches a certain degree despite of longer holding time (ie. longer than 480 min). Similar behavior is also found in the isothermal annealing experiments at 550

α

) from 0.1

Fig. 5. Powder x-ray diffraction patterns of MgB2 samples prepared using different heating conditions. Markers are placed above the peaks corresponding to Mg and MgO impurities. The unmarked peaks correspond to MgB2 (from Ref. [34]).

Recently, a new process, called two-step heat-treatment, has been developed to fabricate undoped MgB2 bulk superconductors [37]. In this process, short high-temperature sintering at 1100 °C is followed by low-temperature annealing. Samples prepared by this method exhibit, uniquely, well-connected small grains with a high level of disorder in the MgB2 phase, which yields an in-field *J*c of nearly one order of magnitude higher than for the samples prepared by single-step sintering at high or low temperature. However, the applicability of the two-step heat-treatment to the fabrication of MgB2 wires has yet to be investigated.

To summarize, these MgB2 superconductors synthesized at low temperature were generally cleaner and denser than the same samples sintered at high temperature due to the reduced volatility and oxidation of Mg, which could improve the connectivity between MgB2 grains. Moreover, sintering at low temperature can also obtain the refined MgB2 grains, which obviously strengthens the grain-boundary pinning. Both of factors are bound to result in the improvement of critical current density in the low-temperature sintered samples compared to the typical high-temperature sintered samples. From this point of view, the lowtemperature synthesis might be the most promise and effective method in obtaining the higher *J*c in MgB2 superconductors. Hence, it makes sense to clarify the phase formation mechanism of MgB2 during the low-temperature sintering.

Fig. 5. Powder x-ray diffraction patterns of MgB2 samples prepared using different heating conditions. Markers are placed above the peaks corresponding to Mg and MgO impurities.

Recently, a new process, called two-step heat-treatment, has been developed to fabricate undoped MgB2 bulk superconductors [37]. In this process, short high-temperature sintering at 1100 °C is followed by low-temperature annealing. Samples prepared by this method exhibit, uniquely, well-connected small grains with a high level of disorder in the MgB2 phase, which yields an in-field *J*c of nearly one order of magnitude higher than for the samples prepared by single-step sintering at high or low temperature. However, the applicability of the two-step heat-treatment to the fabrication of MgB2 wires has yet to be

To summarize, these MgB2 superconductors synthesized at low temperature were generally cleaner and denser than the same samples sintered at high temperature due to the reduced volatility and oxidation of Mg, which could improve the connectivity between MgB2 grains. Moreover, sintering at low temperature can also obtain the refined MgB2 grains, which obviously strengthens the grain-boundary pinning. Both of factors are bound to result in the improvement of critical current density in the low-temperature sintered samples compared to the typical high-temperature sintered samples. From this point of view, the lowtemperature synthesis might be the most promise and effective method in obtaining the higher *J*c in MgB2 superconductors. Hence, it makes sense to clarify the phase formation

The unmarked peaks correspond to MgB2 (from Ref. [34]).

mechanism of MgB2 during the low-temperature sintering.

investigated.
