**3. The effect of Cu activator on the microstructure and superconductive properties of MgB2 prepared by sintering**

Cu addition can improve the sintering efficiency of MgB2 and thus selected as sintering activator. However, whether Cu activator optimizes the microstructure and superconductive properties of MgB2? To answer this question, the effect of Cu activator on the microstructure of MgB2 sintered at both low temperature and high temperature were investigated in detail.

### **3.1 Effect of Cu activator on the reduction of MgO impurity in MgB2 sintered at high temperature**

MgO is always present as the inevitable impurity phase during the sintering process of MgB2 for the reason that Mg is very reactive with oxygen, which can be supplied by the gaseous O impurity in the protective Ar gas and the oxide impurity (such as B2O3 impurity in the B powders) in the starting materials. The presence of MgO impurity may be of great importance and yields a significant effect on the superconductive properties of MgB2 superconductor. Although the MgO nanoinclusions within MgB2 grains could serve as strong flux pinning centers when their size were comparable to the coherent length of MgB2 (.approximately 6~7 nm), the presence of excess MgO phases or largesized MgO particles at the grain boundaries could result in the degradation of grain connectivity [49, 50]. Hence, it is essentially important to control the amount of MgO impurity during the sintering of MgB2 samples.

In our previous work [51], based on the investigation of the effect of minor Cu addition on the phase formation of MgB2, it is found that the minor Cu addition (<3 at %) could apparently reduce the amount of MgO impurity in the prepared MgB2 samples, which provided a new route to govern the oxidation of Mg during the in-situ sintering of MgB2 samples by altering the amount of Cu addition.

Figure 14 shows the X-ray diffraction patterns of the (Mg1.1B2)1-xCux (x = 0.0, 0.01, 0.03 and 0.10) samples sintered at 850oC for 30min. It can be seen that all the sintered samples contain MgB2 as the main phase. In the undoped samples, the MgO peaks are easily recognized, which suggests that some Mg was oxidized during the sintering process and thus MgO was the main impurity in the sintered samples. On the other hand, in the diffracted patterns of the Cu-doped samples, all the MgO phase peaks become weaker and even some peaks identified as MgO phase disappear with the amount of Cu addition increasing. This trend can be observed more clearly from the Fig. 15, which shows the most intense peak (the peak of (200) crystal plane) of MgO in the X-ray diffraction patterns of the sintered (Mg1.1B2)1-xCux (x = 0.0, 0.01 and 0.03) samples. The results suggest that the minor Cu addition can depress the oxidation of Mg apparently during the in-situ sintering of MgB2 samples.

Sintering Process and Its Mechanism of MgB2 Superconductors 489

amount of Cu addition increases from 0.03 to 0.10, the weight fraction of MgO almost remains unchanged (see Fig. 16) while the MgCu2 phase increases significantly (see Fig. 14). The excess Cu addition in the (Mg1.1B2)0.9Cu0.1 sample has no significant effect on the further decrease of MgO impurity. Besides, the excess MgCu2 phase in the (Mg1.1B2)0.9Cu0.1 sample (see Fig. 1) may also depress the superconductivity properties of MgB2 phase. Hence, we conclude that the x=0.03 Cu addition has the best effect on the decrease of MgO impurity

Fig. 16. The weight fraction of MgO versus the amount of Cu addition in the Cu-doped

The scanning electron microscopy images of the sintered (Mg1.1B2)1-xCux samples are shown in the Fig. 17. There is an MgO layer on the partial surface of MgB2 grains in the undoped sample, as shown in Fig. 17a. The MgO layer consists of short MgO whiskers, which is similar with the MgO morphology observed in the study on the oxidation of MgB2 [53]. On the other hand, in the Cu-doped samples, the amount of MgO impurity decreases with the increasing amount of Cu addition and at the same time the morphology of MgO transits from whiskers to nanoparticles (see Fig. 17b and Fig. 17c). The result of SEM images is consistent with the XRD pattern and they both reveal that the addition of minor Cu can apparently decrease the MgO impurity in the MgB2 samples. From Fig. 17, it is also found that the MgB2 grains become larger and more regular accompanying with the increasing amount of Cu addition, which indicates that the Cu addition can also promote the growth of MgB2 grains at the same time with decreasing the MgO impurity in the prepared MgB2

during the in-situ sintering of MgB2 samples.

samples sintered at 850 oC for 30 min [51].

samples.

Fig. 14. X-ray diffraction patterns of the prepared (Mg1.1B2)1-xCux samples sintered at 850oC for 30min with (a) x = 0, (b) x = 0.01, (c) x = 0.03, (d) x=0.10, respectively [51].

Fig. 15. The enlarged X-ray diffraction patterns around (200) of MgO impurity in the (Mg1.1B2)1-xCux samples sintered at 850oC for 30min with (a) x = 0, (b) x = 0.01, (c) x = 0.03, respectively [51].

The weight fraction of MgO was calculated from the X-ray diffraction patterns according to the External Standard Method. Fig. 16 shows the weight fraction of MgO versus the amount of Cu addition in the sintered samples. From the figure, it is found that the weight fraction of MgO in the undoped MgB2 sample is about 16.5%, which is comparable with the previous study [52]. On the other hand, the weight fraction of MgO decreases obviously from 16.5% to 12.5% with the amount of Cu addition increasing from 0.0 to 0.03. However, when the

Fig. 14. X-ray diffraction patterns of the prepared (Mg1.1B2)1-xCux samples sintered at 850oC

Fig. 15. The enlarged X-ray diffraction patterns around (200) of MgO impurity in the (Mg1.1B2)1-xCux samples sintered at 850oC for 30min with (a) x = 0, (b) x = 0.01, (c) x = 0.03,

The weight fraction of MgO was calculated from the X-ray diffraction patterns according to the External Standard Method. Fig. 16 shows the weight fraction of MgO versus the amount of Cu addition in the sintered samples. From the figure, it is found that the weight fraction of MgO in the undoped MgB2 sample is about 16.5%, which is comparable with the previous study [52]. On the other hand, the weight fraction of MgO decreases obviously from 16.5% to 12.5% with the amount of Cu addition increasing from 0.0 to 0.03. However, when the

respectively [51].

for 30min with (a) x = 0, (b) x = 0.01, (c) x = 0.03, (d) x=0.10, respectively [51].

amount of Cu addition increases from 0.03 to 0.10, the weight fraction of MgO almost remains unchanged (see Fig. 16) while the MgCu2 phase increases significantly (see Fig. 14). The excess Cu addition in the (Mg1.1B2)0.9Cu0.1 sample has no significant effect on the further decrease of MgO impurity. Besides, the excess MgCu2 phase in the (Mg1.1B2)0.9Cu0.1 sample (see Fig. 1) may also depress the superconductivity properties of MgB2 phase. Hence, we conclude that the x=0.03 Cu addition has the best effect on the decrease of MgO impurity during the in-situ sintering of MgB2 samples.

Fig. 16. The weight fraction of MgO versus the amount of Cu addition in the Cu-doped samples sintered at 850 oC for 30 min [51].

The scanning electron microscopy images of the sintered (Mg1.1B2)1-xCux samples are shown in the Fig. 17. There is an MgO layer on the partial surface of MgB2 grains in the undoped sample, as shown in Fig. 17a. The MgO layer consists of short MgO whiskers, which is similar with the MgO morphology observed in the study on the oxidation of MgB2 [53]. On the other hand, in the Cu-doped samples, the amount of MgO impurity decreases with the increasing amount of Cu addition and at the same time the morphology of MgO transits from whiskers to nanoparticles (see Fig. 17b and Fig. 17c). The result of SEM images is consistent with the XRD pattern and they both reveal that the addition of minor Cu can apparently decrease the MgO impurity in the MgB2 samples. From Fig. 17, it is also found that the MgB2 grains become larger and more regular accompanying with the increasing amount of Cu addition, which indicates that the Cu addition can also promote the growth of MgB2 grains at the same time with decreasing the MgO impurity in the prepared MgB2 samples.

Sintering Process and Its Mechanism of MgB2 Superconductors 491

In order to investigate the effect of the decreasing MgO impurity induced by the minor Cu addition on the superconductive properties of MgB2 samples, the corresponding *Tc* temperatures of all sintered samples were measured. Fig. 18 illustrates the temperature dependence of resistivity for the (Mg1.1B2)1-xCux (with x = 0, 0.01 and 0.03) samples sintered at 850 oC for 30min. As shown in it, the undoped sample exhibits a slight suppression in the value of *Tc* compared to the typical pure MgB2 samples, which can be attributed to the limit of MgB2 intergranular connection caused by the excessive MgO impurity at the grain boundaries. However, in the Cu-doped samples, the values of *Tc* are over 38K and slightly increase from 38.1 K to 38.6 K with the increasing amount of Cu addition from x = 0.01 to x = 0.03, which is comparable to the pure MgB2 samples (39 K). The observation could be explained by the decrease of MgO impurity and the growth of MgB2 grains resulting from

Fig. 18. The temperature dependence of resistivity for the (Mg1.1B2)1-xCux (x = 0, 0.01 and

In summary, the minor Cu addition can decrease the amount of MgO impurity and thus significantly improve the superconductive properties of MgB2 bulks. However, how the Cu addition avoids the oxidation of Mg during the sintering process of MgB2 is still to be

It has been indicated that during the sintering process of Mg-Cu-B system, the Mg-Cu liquid locally formed firstly in the presence of Cu through an eutectic reaction. The local Mg-Cu liquid appearing at such low temperature could dissolve some Mg and wrap the neighboring Mg particles, which partly avoided Mg contacting with the gaseous O existing in the interspace of the pressed samples and the oxide impurity (such as B2O3 in the B powders) in the starting materials. Hence, the oxidation of Mg during the low-temperature (below the Mg melting point) sintering stage resulting from the gaseous O existing in the

0.03) samples sintered at 850 oC for 30min [51].

answered.

the minor Cu addition.

Fig. 17. Scanning electron microscopy images of the (Mg1.1B2)1-xCux samples sintered at 850 oC for 30 min with (a) x = 0, (b) x = 0.01 and (c) x = 0.03, respectively. The MgO whiskers and nanoparticles are indicated by the black circles and arrows in the figures [51].

Fig. 17. Scanning electron microscopy images of the (Mg1.1B2)1-xCux samples sintered at 850 oC for 30 min with (a) x = 0, (b) x = 0.01 and (c) x = 0.03, respectively. The MgO whiskers

and nanoparticles are indicated by the black circles and arrows in the figures [51].

c

b

a

In order to investigate the effect of the decreasing MgO impurity induced by the minor Cu addition on the superconductive properties of MgB2 samples, the corresponding *Tc* temperatures of all sintered samples were measured. Fig. 18 illustrates the temperature dependence of resistivity for the (Mg1.1B2)1-xCux (with x = 0, 0.01 and 0.03) samples sintered at 850 oC for 30min. As shown in it, the undoped sample exhibits a slight suppression in the value of *Tc* compared to the typical pure MgB2 samples, which can be attributed to the limit of MgB2 intergranular connection caused by the excessive MgO impurity at the grain boundaries. However, in the Cu-doped samples, the values of *Tc* are over 38K and slightly increase from 38.1 K to 38.6 K with the increasing amount of Cu addition from x = 0.01 to x = 0.03, which is comparable to the pure MgB2 samples (39 K). The observation could be explained by the decrease of MgO impurity and the growth of MgB2 grains resulting from the minor Cu addition.

Fig. 18. The temperature dependence of resistivity for the (Mg1.1B2)1-xCux (x = 0, 0.01 and 0.03) samples sintered at 850 oC for 30min [51].

In summary, the minor Cu addition can decrease the amount of MgO impurity and thus significantly improve the superconductive properties of MgB2 bulks. However, how the Cu addition avoids the oxidation of Mg during the sintering process of MgB2 is still to be answered.

It has been indicated that during the sintering process of Mg-Cu-B system, the Mg-Cu liquid locally formed firstly in the presence of Cu through an eutectic reaction. The local Mg-Cu liquid appearing at such low temperature could dissolve some Mg and wrap the neighboring Mg particles, which partly avoided Mg contacting with the gaseous O existing in the interspace of the pressed samples and the oxide impurity (such as B2O3 in the B powders) in the starting materials. Hence, the oxidation of Mg during the low-temperature (below the Mg melting point) sintering stage resulting from the gaseous O existing in the

Sintering Process and Its Mechanism of MgB2 Superconductors 493

Moreover, the supersaturation of MgB2 in the Mg-Cu liquid must be high enough for the two dimensional nucleation due to the comparable less amount of Mg-Cu liquid (the amount of Cu addition is only 8 at%). Hence, it is proposed that the formation mechanism of the present lamellar MgB2 grains is attributed to the two dimensional nucleation. The energy

> 2 22 ( / ) exp( /65 ) *C Ce crit* = Ω π

(/ ) *C Ce crit* is the critical supersaturation, *h* is the step height, *Ω* is the atomic volume, *r* is the surface energy of crystal, *k* is the Boltzmann constant and *T* is the sintering temperature. It can be seen that the energy barrier of the two dimensional nucleation mainly depends

Fig. 19. The SEM images of sintered samples with (a) the Cu-doped sample sintered at

575 oC for 5h and (b) the undoped sample sintered at 750 oC for 1h [56].

*h r kT* (6)

**(a)**

**(b)**

barrier of the two dimensional nucleation could be defined as follows:

interspace and the oxide impurity in the starting materials can be depressed by the presence of local Mg-Cu liquid significantly.

When the temperature was above the Mg melting point (about 650 oC) during the sintering process, the unreacted Mg after the solid reaction stage would melt and volatilize severely as a result of the high vapor pressure of Mg liquid. The gaseous Mg mixed with the protective Ar gas and could react with the O2 impurity in the protective Ar gas at such high temperature, which resulted in the increasing amount of MgO impurity deposited in the undoped MgB2 samples after cooling to room temperature [54], as shown in Fig. 17a. On the other hand, the Cu addition could lower the melting point of Mg at the same time of decreasing the vapor pressure of Mg liquid at high temperature [55]. The decrease of the vapor pressure of Mg liquid led by the Cu addition could reduce the amount of the gaseous Mg from the volatilization of Mg, which thus decrease the amount of MgO impurity resulting from the oxidation of gaseous Mg in the doped samples (as shown in Fig. 17b and 17c).

#### **3.2 The synthesis of lamellar MgB2 crystalline by Cu activated sintering at low temperature**

The microstructure of MgB2 synthesized by Cu activated sintering at low temperature was also investigated in detail [56]. The SEM images of both sintered Cu-doped sample and undoped sample are illustrated in Fig. 19. Lamellar MgB2 grains with typical hexagonal shape were observed in the Cu-doped sample sintered at low temperature (see Fig. 19a, denoted by the black arrows). There are few impurities between lamellar MgB2 grains in the MgB2 region and the Mg-Cu impurities mainly distribute in the region near the lamellar MgB2 grains, as shown in Fig. 19a. One can also find that all of the MgB2 grains in the lamellar structure almost share the same orientation except only a few of them. On the other hand, the MgB2 grains in the undoped sample sintered at high temperature are nearly in the same size as those in the Cu-doped samples and most of them also exhibit typical hexagonal shape. But their orientation is random, which is the typical characteristic of MgB2 grains sintered in the traditional solid-state sintering (see Fig. 19b). Hence, the MgB2 grains in the lamellar structure seem to be in better connectivity with each other and there are also fewer voids between them when compared to the MgB2 grains in the random orientation, as shown in Fig. 19.

It is proposed that Mg atoms could easily diffuse into B through the path of local Mg-Cu liquid and then react with B forming MgB2 at the interface between Mg-Cu liquid and B particles. Since the local Mg-Cu liquid only serves as the path for the diffusion of Mg into B and does not react with B until all the Mg is run out, it is always present and provide the constant liquid environment for the nucleation and growth of MgB2 grains. As we all known, there are two main mechanism forming the lamellar crystalline in the liquid sintering environment, two dimensional nucleation and screw dislocation nucleation. The concentration gradient is the driving force for both mechanisms during the isothermal liquid sintering. The surface of the grains in the lamellar crystalline formed following the two dimensional nucleation are generally more smooth and regular than the screw dislocation [57]. On the other hand, the two dimensional nucleation also needs higher supersaturation than the screw dislocation [58]. In present case, the surface of MgB2 grains in the lamellar crystalline is smooth and regular and no obvious dislocations and impurities are observed.

interspace and the oxide impurity in the starting materials can be depressed by the presence

When the temperature was above the Mg melting point (about 650 oC) during the sintering process, the unreacted Mg after the solid reaction stage would melt and volatilize severely as a result of the high vapor pressure of Mg liquid. The gaseous Mg mixed with the protective Ar gas and could react with the O2 impurity in the protective Ar gas at such high temperature, which resulted in the increasing amount of MgO impurity deposited in the undoped MgB2 samples after cooling to room temperature [54], as shown in Fig. 17a. On the other hand, the Cu addition could lower the melting point of Mg at the same time of decreasing the vapor pressure of Mg liquid at high temperature [55]. The decrease of the vapor pressure of Mg liquid led by the Cu addition could reduce the amount of the gaseous Mg from the volatilization of Mg, which thus decrease the amount of MgO impurity resulting from the oxidation of gaseous Mg in the doped samples (as shown in Fig. 17b and

**3.2 The synthesis of lamellar MgB2 crystalline by Cu activated sintering at low** 

The microstructure of MgB2 synthesized by Cu activated sintering at low temperature was also investigated in detail [56]. The SEM images of both sintered Cu-doped sample and undoped sample are illustrated in Fig. 19. Lamellar MgB2 grains with typical hexagonal shape were observed in the Cu-doped sample sintered at low temperature (see Fig. 19a, denoted by the black arrows). There are few impurities between lamellar MgB2 grains in the MgB2 region and the Mg-Cu impurities mainly distribute in the region near the lamellar MgB2 grains, as shown in Fig. 19a. One can also find that all of the MgB2 grains in the lamellar structure almost share the same orientation except only a few of them. On the other hand, the MgB2 grains in the undoped sample sintered at high temperature are nearly in the same size as those in the Cu-doped samples and most of them also exhibit typical hexagonal shape. But their orientation is random, which is the typical characteristic of MgB2 grains sintered in the traditional solid-state sintering (see Fig. 19b). Hence, the MgB2 grains in the lamellar structure seem to be in better connectivity with each other and there are also fewer voids between them when compared to the MgB2 grains in the random orientation, as

It is proposed that Mg atoms could easily diffuse into B through the path of local Mg-Cu liquid and then react with B forming MgB2 at the interface between Mg-Cu liquid and B particles. Since the local Mg-Cu liquid only serves as the path for the diffusion of Mg into B and does not react with B until all the Mg is run out, it is always present and provide the constant liquid environment for the nucleation and growth of MgB2 grains. As we all known, there are two main mechanism forming the lamellar crystalline in the liquid sintering environment, two dimensional nucleation and screw dislocation nucleation. The concentration gradient is the driving force for both mechanisms during the isothermal liquid sintering. The surface of the grains in the lamellar crystalline formed following the two dimensional nucleation are generally more smooth and regular than the screw dislocation [57]. On the other hand, the two dimensional nucleation also needs higher supersaturation than the screw dislocation [58]. In present case, the surface of MgB2 grains in the lamellar crystalline is smooth and regular and no obvious dislocations and impurities are observed.

of local Mg-Cu liquid significantly.

17c).

**temperature** 

shown in Fig. 19.

Moreover, the supersaturation of MgB2 in the Mg-Cu liquid must be high enough for the two dimensional nucleation due to the comparable less amount of Mg-Cu liquid (the amount of Cu addition is only 8 at%). Hence, it is proposed that the formation mechanism of the present lamellar MgB2 grains is attributed to the two dimensional nucleation. The energy barrier of the two dimensional nucleation could be defined as follows:

$$(\text{C} / \text{C}e)\_{crit} = \exp(\pi h \Omega r^2 \,/\, 65k^2 T^2) \tag{6}$$

(/ ) *C Ce crit* is the critical supersaturation, *h* is the step height, *Ω* is the atomic volume, *r* is the surface energy of crystal, *k* is the Boltzmann constant and *T* is the sintering temperature. It can be seen that the energy barrier of the two dimensional nucleation mainly depends

Fig. 19. The SEM images of sintered samples with (a) the Cu-doped sample sintered at 575 oC for 5h and (b) the undoped sample sintered at 750 oC for 1h [56].

Sintering Process and Its Mechanism of MgB2 Superconductors 495

(c)

Fig. 21 shows the temperature dependence of resistivity of the Cu-doped sample and undoped sample. The resistivity of the Cu-doped samples is much lower than the undoped sample in the measured temperature region from 300K to 40K. The resistivity of MgB2 sample should be increased with the addition of Cu, as reported previously [59]. Since the Mg-Cu alloys mainly concentrate around the voids and do not degrade the grain connectivity of MgB2 phase in present sample, the resistivity is ought to keep unchanged and should not be lower than the undoped sample. Hence, the abnormal low resistivity

Fig. 21. The temperature dependence of resistivity of the Cu-doped sample and undoped

Fig. 20. The schematic of the formation mechanism of the lamellar MgB2 crytalline with (a) the initial stage, (b) the nucleation and growth stage and (c) the final stage [56].

must be attributed to the lamellar structure of MgB2 grains.

sample [56].

on the step height and the surface energy of MgB2 crystal. On the other hand, only when the MgB2 supersaturation in the Mg-Cu liquid is higher than the critical supersaturation, the nucleation can start on the surface of B and form the new step. After that, the MgB2 grains easily grow at this step and form a crystal layer. Accordingly, the schematic of the formation mechanism of the lamellar MgB2 crytalline is shown in the Fig. 20 with (a) the initial stage, (b) the nucleation and growth stage and (c) the final stage. At the initial stage, the Mg that diffused to the surface of B through the Mg-Cu liquid would react with B as below: Mg + 2B = MgB2, which can result in the concentration gradient of Mg in the interface (see Fig. 20a). As a result, a lot of Mg could diffuse into the interface and react with B forming MgB2. Most of produced MgB2 is dissolved in the Mg-Cu liquid and some MgB2 will be physically absorbed on the surface of B. When the MgB2 supersaturation is higher than the critical value for the nucleation, these absorbed MgB2 will form two dimensional nuclei and produce a new step through the thermodynamic fluctuation. And then the dissolved MgB2 will deposit on this step and the MgB2 grains could rapidly grow on this step and form the crystal layer (see Fig. 20b). The new nuclei will continuously forming on the surface of MgB2 crystal layer and then a new crystal layer will form again. As a result, the lamellar MgB2 grains are obtained (see Fig. 20c).

on the step height and the surface energy of MgB2 crystal. On the other hand, only when the MgB2 supersaturation in the Mg-Cu liquid is higher than the critical supersaturation, the nucleation can start on the surface of B and form the new step. After that, the MgB2 grains easily grow at this step and form a crystal layer. Accordingly, the schematic of the formation mechanism of the lamellar MgB2 crytalline is shown in the Fig. 20 with (a) the initial stage, (b) the nucleation and growth stage and (c) the final stage. At the initial stage, the Mg that diffused to the surface of B through the Mg-Cu liquid would react with B as below: Mg + 2B = MgB2, which can result in the concentration gradient of Mg in the interface (see Fig. 20a). As a result, a lot of Mg could diffuse into the interface and react with B forming MgB2. Most of produced MgB2 is dissolved in the Mg-Cu liquid and some MgB2 will be physically absorbed on the surface of B. When the MgB2 supersaturation is higher than the critical value for the nucleation, these absorbed MgB2 will form two dimensional nuclei and produce a new step through the thermodynamic fluctuation. And then the dissolved MgB2 will deposit on this step and the MgB2 grains could rapidly grow on this step and form the crystal layer (see Fig. 20b). The new nuclei will continuously forming on the surface of MgB2 crystal layer and then a new crystal layer will form again. As a result, the lamellar MgB2

(a)

(b)

grains are obtained (see Fig. 20c).

Fig. 20. The schematic of the formation mechanism of the lamellar MgB2 crytalline with (a) the initial stage, (b) the nucleation and growth stage and (c) the final stage [56].

Fig. 21 shows the temperature dependence of resistivity of the Cu-doped sample and undoped sample. The resistivity of the Cu-doped samples is much lower than the undoped sample in the measured temperature region from 300K to 40K. The resistivity of MgB2 sample should be increased with the addition of Cu, as reported previously [59]. Since the Mg-Cu alloys mainly concentrate around the voids and do not degrade the grain connectivity of MgB2 phase in present sample, the resistivity is ought to keep unchanged and should not be lower than the undoped sample. Hence, the abnormal low resistivity must be attributed to the lamellar structure of MgB2 grains.

Fig. 21. The temperature dependence of resistivity of the Cu-doped sample and undoped sample [56].

Sintering Process and Its Mechanism of MgB2 Superconductors 497

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According to the Rowell connectivity analysis, the calculated active cross-sectional area fraction (*AF*) represents the connectivity factor between adjacent grains [60]. Here the *AF* is estimated as:

$$\mathbf{A\_F} = \Delta \left\| \mathbf{p}\_{\text{ideal}} \right\| \left( \mathbf{p}\_{\text{700K}} - \mathbf{p}\_{40\text{K}} \right) \tag{7}$$

$$
\Delta \blacktriangleright \mathfrak{p}\_{\text{ideal}} = \mathfrak{p}\_{\text{ideal}(\text{300K})} \text{ - } \blacktriangleright \mathfrak{p}\_{\text{ideal}(\text{400K})} \tag{8}
$$

Where *ρ ideal* is the resistivity of a reference crystal and *ρT* is our measured resistivity at temperature *T*.

According to the previous studies [13, 60, 61], here the ∆ *ρ ideal* is 7.3 μΩcm. The results are listed in the Table 3. The value of *AF* in the present undoped sample is comparable to that of samples sintered under the similar condition in previous reports [60]. The Cu-doped sample exhibits very excellent *AF*, more than two times higher than that of the undoped samples. To further analyze the intergrain connectivity, the residual resistivity ratio (RRR) defined by *ρ 300K / ρ 40K* was also estimated, as shown in Table 3. All of the above results indicate that the lamellar MgB2 grains possess much better grain connectivity than the typical morphology of MgB2 grains. It should be pointed out that the onset of the transition temperature (*Tc*(onset)) of the Cu-doped sample is higher than that of undoped samples, which might be due to better connectivity and higher crystallinity of the lamellar grains (see Fig. 20a and Fig. 20b). However, the width of transition (∆*Tc*) of the Cu-doped sample becomes a little wider than that of undoped sample. The transition broadening can be caused by the small grain size, inhomogeneity, impurities and so on. In present case, the lamellar MgB2 grains shared the same orientation and lead to the intrinsic inhomogeneity in the doped sample, which could be the main factor broadening the transition width.


Table 3 The transition temperature (*Tc*(onset)), width of transition (∆*Tc*), measured resistivity values, residual resistivity ratio (RRR) and active cross-sectional area fraction (*AF*) for Cudoped sample and undoped sample, respectively.

In summary, the lamellar MgB2 grains can be obtained by Cu-activated sintering at low temperature. This lamellar MgB2 grains possess much better grain connectivity than the typical morphology of MgB2 grains synthesized by the traditional solid-state sintering. Together with the proper methods increasing the pinning, the present lamellar MgB2 grains might result in the further improvement of *Jc*.

#### **4. References**


According to the Rowell connectivity analysis, the calculated active cross-sectional area fraction (*AF*) represents the connectivity factor between adjacent grains [60]. Here the *AF* is

AF = ∆ ρ ideal / (ρ 300K – ρ 40K ) (7)

Where *ρ ideal* is the resistivity of a reference crystal and *ρT* is our measured resistivity at

According to the previous studies [13, 60, 61], here the ∆ *ρ ideal* is 7.3 μΩcm. The results are listed in the Table 3. The value of *AF* in the present undoped sample is comparable to that of samples sintered under the similar condition in previous reports [60]. The Cu-doped sample exhibits very excellent *AF*, more than two times higher than that of the undoped samples. To further analyze the intergrain connectivity, the residual resistivity ratio (RRR) defined by *ρ 300K / ρ 40K* was also estimated, as shown in Table 3. All of the above results indicate that the lamellar MgB2 grains possess much better grain connectivity than the typical morphology of MgB2 grains. It should be pointed out that the onset of the transition temperature (*Tc*(onset)) of the Cu-doped sample is higher than that of undoped samples, which might be due to better connectivity and higher crystallinity of the lamellar grains (see Fig. 20a and Fig. 20b). However, the width of transition (∆*Tc*) of the Cu-doped sample becomes a little wider than that of undoped sample. The transition broadening can be caused by the small grain size, inhomogeneity, impurities and so on. In present case, the lamellar MgB2 grains shared the same orientation and lead to the intrinsic inhomogeneity in the doped sample, which could

∆ ρ ideal = ρ ideal(300K) - ρ ideal(40K) (8)

estimated as:

temperature *T*.

samples

Undoped

Cu-doped

**4. References** 

63-64.

be the main factor broadening the transition width.

doped sample and undoped sample, respectively.

might result in the further improvement of *Jc*.

*Tc*(onset) (K)

*ρ 40K* (μΩcm)

MgB2 0.25 38.0 18.388 51.449 2.780 0.221

MgB2 0.40 38.3 5.980 18.355 3.069 0.590 Table 3 The transition temperature (*Tc*(onset)), width of transition (∆*Tc*), measured resistivity values, residual resistivity ratio (RRR) and active cross-sectional area fraction (*AF*) for Cu-

In summary, the lamellar MgB2 grains can be obtained by Cu-activated sintering at low temperature. This lamellar MgB2 grains possess much better grain connectivity than the typical morphology of MgB2 grains synthesized by the traditional solid-state sintering. Together with the proper methods increasing the pinning, the present lamellar MgB2 grains

[1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zentani and J. Akimitsu: Nature, 2001 410

[2] D.C. Larbalestier, L.D. Cooley, M.O. Rikel, A.A. Polyanskii, J. Jiang, S. Patnaik, X.Y. Cai,

D.M. Feldmann, A. Gurevich, A.A. Squitieri, M.T. Naus, C.B. Eom, E.E. Hellstrom,

*ρ 300K*

(μΩcm) RRR *AP* 

∆ *Tc* (K)

R.J. Cava, K.A. Regan, N. Rogado, M.A. Hayward, T. He, J.S. Slusky, P. Khalifah, K. Inumaru and M. Haas: Nature, 2001 410 186-189.


**Part 7** 

**Dielectrics and Opto-Electronic Materials** 

