Towards the Realization of Higher Connectivity in MgB2 Conductors:
In-situ or Sintered Ex-situ?
Akiyasu Yamamoto1,3*, Hiroya Tanaka1, Jun-ichi Shimoyama1, Hiraku Ogino1, Kohji
Kishio1 and Teruo Matsushita2
1Department of Applied Chemistry, The University of Tokyo, 7-3-1 Hongo, Bunkyo,
Tokyo 113-8656, Japan
2Faculty of Computer Science and Systems Engineering, Kyushu Institute of
Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan
3Japan Science and Technology Agency, PRESTO, 4-1-8 Honcho Kawaguchi, Saitama
*E-mail address: firstname.lastname@example.org
The two most common types of MgB2 conductor fabrication technique - in-situ and
ex-situ - show increasing conflicts concerning the connectivity, an effective
current-carrying cross-sectional area. An in-situ reaction yields a strong intergrain
coupling with a low packing factor, while an ex-situ process using pre-reacted MgB2
yields tightly packed grains, however, their coupling is much weaker. We studied the
normal-state resistivity and microstructure of ex-situ MgB2 bulks synthesized with
varied heating conditions under ambient pressure. The samples heated at moderately
high temperatures of ~900°C for a long period showed an increased packing factor, a
larger intergrain contact area and a significantly decreased resistivity, all of which
indicate the solid-state self-sintering of MgB2. Consequently the connectivity of the
sintered ex-situ samples exceeded the typical connectivity range 5-15% of the in-situ
samples. Our results show self-sintering develops the superior connectivity potential of
ex-situ MgB2, though its intergrain coupling is not yet fulfilled, to provide a strong
possibility of twice or even much higher connectivity in optimally sintered ex-situ
MgB2 than in in-situ MgB2.
One of the distinct characteristics of MgB2 among the
high-temperature-superconductors (HTSs) is its conventional metallic superconductivity,
i.e., s-wave symmetry of pairing, high carrier density, long and rather isotropic
coherence length, together with the high critical temperature Tc=40 K and high upper
critical field Bc2>50 T . These characteristics bring in a strongly linked current flow
in randomly oriented polycrystals  and an easy fabrication of long length wires by the
common power-in-tube (PIT) method. Additionally, being a simple intermetallic line
compound from two light elements, Mg and B, and an inexpensive material costs push
MgB2 to a strong candidate for next-generation superconducting materials to be
operated at liquid-helium-free temperatures of 15-20 K.
The reported values of critical current density Jc at 20 K for MgB2 bulks, wires
and tapes 105–106 Acm−2 [3-5] turned out to be apparently lower than the depairing
current density, Jd(20 K)~Bc/0~108 Acm−2, where Bc is the thermodynamic critical
field, 0 is the permeability of vacuum and is the penetration depth. Indeed very high
Jc values reaching 107 Acm−2 at 20 K have been reported for epitaxial thin films [6,7].
Grain boundaries work as predominant flux pinning centers in MgB2 and the doping of
carbon-based compounds, such as graphite [8,9], B4C , SiC , and organic
compounds [12-14] and low-temperature synthesis  are reported to be effective in
increasing Jc. The degradation of crystallinity, i.e., the distortion of honeycomb boron
lattice, is believed to be the origin of the enhancement of flux pinning for both cases and
particularly contributes to the improvement of Jc under high magnetic fields [16,17].
A reduction in the effective current-carrying cross-sectional area of the sample
was suggested by Rowell to explain the large gap of Jc between films and wires .
The Josephson junction model of the grain boundaries , the two-band model [19,20],
the anisotropy model , and the oxide barrier model  were considered to affect
the limited transport properties of MgB2. In our previous study, we applied a mean-field
theory to the three-dimensional percolation problem to understand the anomaly
suppressed connectivity in rather weak-link-free MgB2 polycrystals [23,24]. The
mean-field theory quantitatively showed that the packing factor (P) of polycrystals,
impurity layers at grain boundaries, and anisotropy are the limiting factors of the
In-situ and ex-situ methods have been developed to manufacture MgB2 bulks,
wires, and tapes. Perhaps the most commonly studied method is the in-situ method, that
is the formation of MgB2 simply from mixed powders of Mg+2B, since a relatively high
Jc value is easily attained owing to its reasonably strong intergrain coupling. In an
in-situ reaction process, Mg grains melt and diffuse into B grains, and transform into
voids resulting in a low bulk density (P~50%) and a low connectivity. On the other hand,
the ex-situ method using prereacted MgB2 powder is favorable in terms of bulk density.
A packing factor close to ~75% (the close packing of spheres) can be expected. Even
unsintered, as-pressed ex-situ MgB2 tapes show a relatively high transport Jc value of
~104 Acm−2 at 20 K . Heat treatment after cold working is effective in improving Jc
through the strengthening of intergrain coupling [3,26-28]. The Jc of heat treated ex-situ
MgB2 is, however, generally lower than that of in-situ MgB2, likely due to the fact that
intergrain coupling is insufficient compared with the strong coupling in the in-situ
MgB2. The connectivity of reasonably high Jc ex-situ MgB2 tapes is reported to be less
than 10% [29,30], which is obviously lower than the typical connectivity of in-situ
MgB2, 5-15% [23,31]. Since the packing factor of ex-situ MgB2 is higher than that of
in-situ MgB2, a better connectivity, even higher than that of in-situ, is naturally expected
if a strong intergrain coupling is achieved.
In this paper we carefully investigated the microstructure, normal-state
resistivity and electrical connectivity of ex-situ MgB2 polycrystalline bulks prepared
using systematically varied heating conditions under ambient pressure. In particular we
employed long heat treatments at high temperatures of ~900°C to promote the
self-sintering of MgB2 grains. In order to prevent the decomposition of MgB2 by the
vaporization of Mg at high temperatures, prereacted MgB2 powders were sealed and
heated in a metal sheath using our powder-in-closed-tube (PICT) technique . We
observed evidence for the solid-state self-sintering of MgB2 and its strong effect on the
enhancement of connectivity. On the basis of the results, we will compare the intergrain
coupling nature of in-situ and ex-situ MgB2, and discuss the prospects for further
improvement of connectivity in MgB2 conductors.
2. Experimental Procedure
Ex-situ MgB2 polycrystalline bulk samples were fabricated by the PICT
method. The detailed fabrication methods for the bulk samples can be found elsewhere
[32,33]. Laboratory-made MgB2 powder or commercially available MgB2 powder (99%
purity, several tens of microns in size, Alfa Aesar) was used as a starting material. The
MgB2 powder was filled into a stainless-steel (SUS316) tube, then the tube was
uniaxially pressed under 500 MPa with both ends closed by mechanical pressing.
Finally each tube was heated at 750-950°C for 3-96 h in an evacuated quartz ampoule.
Laboratory-made MgB2 powder was prepared by grinding the in-situ-processed bulk
(heating condition: 900°C for 2 h) synthesized from mixed powders of Mg (99.5%
purity) and B (99% purity) with the molar ratio of 1:2. In-situ- and diffusion-processed
bulks were prepared from Mg and B powders for comparison.
Constituent phases of the samples were analyzed by the powder x-ray
diffraction (XRD) method using Cu K radiation. Microstructural observation was
performed using a scanning electron microscope (SEM; JEOL JSM-7000F). The
packing factor (P) of the samples was measured with a micrometer caliper and a
weighing balance. Resistivity measurements were performed by the conventional
four-point probe method with ac current of 15 Hz using a physical property
measurement system (PPMS; Quantum Design PPMS Model 6000).
3. Results and Discussion
3. 1. Resistivity and connectivity
Figure 1(a) shows the electrical resistivity as a function of temperature for
the ex-situ bulks from laboratory-made MgB2 powder with a systematically varied
degree of sintering, by heating at different temperatures from 750 to 900°C. The
as-pressed MgB2 bulk before heat treatment, in-situ bulk, and diffusion bulk are also
shown for comparison. The as-pressed bulk has a large resistivity of ~1×104 cm at
room temperature and shows an unusual temperature dependence with a very slight
upturn below ~100 K, resulting in low RRR=(300 K)/(40 K)=1.1. The resistivity of
the as-pressed bulk does start dropping at ~39 K and reaches zero resistance; however,
its superconducting transition is broad with Tc>10 K [Fig. 1(b)]. The high , small
RRR, and large Tc suggest that intergrain coupling is weak. On the other hand, the
ex-situ bulks heat-treated at above 850°C show a successively lower resistivity as the
heat treatment temperature increases, indicative of evolution of intergrain coupling by
sintering. Indeed we observed an increase in packing factor for the heat-treated bulks
compared to the as-pressed bulk. The bulk heated at 900°C for 48 h, with the highest
degree of sintering, shows resistivities of 50 cm at 300 K and 15 cm at 40 K,
which are 2 or 3 orders of magnitude lower than that of the as-pressed bulk and even
lower than that of the typical in-situ bulk. Consequently the resistive transition becomes
sharper with the progression of sintering, and the bulks sintered above 850°C show
small Tc<1 K which is comparable to that of the in-situ bulks.
The evolution of transport current connectivity by sintering is summarized in
Fig. 2. The zero resistance temperature TR0 is defined by <10-1 cm. The electrical
connectivity K = g/, where g=g(300 K)-g(40 K)≡6.32 cm  and
=(300 K)-(40 K) are the difference in resistivity of the ideal MgB2 grains and that
of a sample, respectively, is plotted as a function of sintering temperature. Both TR0 and
K show a rapid increase above 850°C, and the maximum connectivity is obtained for the
bulk sintered at 900°C. Sintering above 950°C reduces connectivity, probably due to the
decomposition of MgB2 as evidenced by B-rich impurity phases observed by
compositional analyses (not shown here). The prolonged heat treatment further
promoted sintering and improvement in connectivity. The bulk sintered at 900°C for 48
h shows K~18% which is among the highest values for MgB2 polycrystals except
samples synthesized by diffusion process [23,34] or under high pressure . Here the
connectivity of the sintered ex-situ bulks exceeds the typical range of in-situ processed
bulks and wires which is 5-15%.
3. 2. Microstructure
Figure 3 summarizes typical microstructural features of MgB2 polycrystalline
bulks prepared by in-situ [Fig. 3(a)] and ex-situ [Fig. 3(b)] methods. Here, gray, black,
and white contrasts in the secondary electron images correspond to MgB2 grains, pores,
and impurity phases, such as MgO, respectively. The in-situ-processed sample shows a
porous microstructure with large voids typically 10-50 m in size. Spaces filled with
Mg powders before the heat treatment transform into voids through the reaction with B.
On the other hand, a characteristic microstructure different from that of the in-situ bulk
can be seen in the ex-situ bulk sintered at 900°C for 24 h. In Fig. 3(b) islands of MgB2
grains and particles with a size of ~10 m are dispersed and the voids occupy the gap
between the islands. For the ex-situ bulk, the shape of the voids is apparently different
from that of the in-situ bulk, and their size is much smaller (typically less than 10 m).
One can see that the intergrain coupling between MgB2 grains/particles is poor in
contrast to that in the in-situ sample where a strongly linked network of MgB2 grains is
observed. The weak intergrain coupling is considered to be the reason for the rather
restricted K observed in the ex-situ bulk [Fig. 1(a)] though the packing factor of the
ex-situ bulk (64%) is much higher than that of the in-situ bulk (48%).
Higher magnification images of the polished cross-sectional surface of MgB2
bulks are shown in Fig. 4 to manifest intergrain coupling between MgB2 grains. The
as-pressed MgB2 bulk before sintering shows fine MgB2 grains/particles are tightly
packed and neither of intergrain or grain-particle coupling can be seen [Fig. 4(b)]. After
heating at 900°C, the surface area of MgB2 grains decreased and the size of voids
increased compared with those observed in the as-pressed and coupling between MgB2
grains/particles were also clearly observed [Fig. 4(c)], all of these suggest that
solid-state self-sintering occurred during the heat treatment. On this magnification scale,
we did not observe impurity phases or cracks at grain boundaries of the sintered ex-situ
MgB2 bulk. Though the area of coupling between grains in the sintered ex-situ bulk is
smaller than that in the in-situ bulk [Fig. 4(a)] such coupling is believed to contribute
significantly as an effective path for the transport current in both normal and
It is well known that the Jc of the ex-situ MgB2 can be largely enhanced by heat
treatment. The improvement of intergrain coupling by sintering or the removal of
volatile impurities from grain boundaries can be considered as the reason. However,
there are few reports on the self-sintering of MgB2. Dancer et al. studied the effects of a
range of heat treatment (widely varied from 200 to 1100°C for 1 h) on the packing
factor and the amount of the MgO impurity phase for ex-situ MgB2 bulks . After
heat treatments they observed little sign of sintering even at 1100°C and a small change
(<3%) in packing factor. Our bulk samples showed a partially sintered microstructure
which is similar to that of spark-plasma-sintered (SPS)  or high-pressure-processed
[35,38] bulks together with an approximately 10% increase in packing factor. The
lowered resistivity by the orders of magnitude observed in the ex-situ bulks suggests
that solid-state self-sintering occurs with a long-period heat treatment at high
temperatures of ~900°C.
Thermodynamically decomposition of MgB2 takes place under a low Mg
partial pressure  as
2MgB2(s) ⇔ MgB4(s) + Mg(g). (1)
Such a decomposition of MgB2 was experimentally observed by the loss of gaseous Mg
at temperatures as low as ~610°C , and the formation of MgB4 obviously causes the
degradation of superconducting properties . In our case, we heated the samples in a
closed system, i.e., a sealed stainless-steel tube, using the PICT method and precisely
controlled the amount of Mg by preventing vaporization. A significant reaction between
vaporized Mg and quartz ampoule occurred when the stainless-steel tube was not sealed.
By using the PICT technique, we did not observe a trace of B-rich phases in the sintered
bulks except samples heated for a very long period where the reaction between the
stainless-steel sheath and Mg occurred. Therefore the sintering of MgB2 should be
performed under precisely controlled conditions of highly reactive, volatile Mg.
We show in Fig. 5 the relationship between packing factor P and the
connectivity K for ex-situ bulks synthesized from both commercial and laboratory-made
powders and heated at 900°C for different periods and in-situ bulks . A higher
connectivity was observed with an increase in P through sintering, and a trend between
P and K was observed for the ex-situ bulks. Note that the data for the ex-situ bulks
shown in Fig. 5 are some of the well-connected samples which exclude those of samples
showing indications of B-rich phase formation. K for the samples with insufficient
sintering or with impurity phases scatters below such a trend. For in-situ MgB2, the
relationship between P and K can be well explained by the mean-field theory for a
three-dimensional site percolation system according to the equation 
where a is the fraction of effective MgB2 grains that can carry current and Pc is the
critical packing factor and is 0.3117 for the three-dimensional cubic site system .
Interestingly, the observed P-K trend for the ex-situ bulks shifts to higher P values than
that for the in-situ bulks, suggesting that the limiting mechanisms of connectivity for the
bulks from two processes are different. Suppose the three-dimensional percolation
model works for the ex-situ bulks, the result indicates that either critical packing factor
Pc is higher and/or intergrain coupling between MgB2 grains/particles (which
corresponds to a) is weaker in the sintered ex-situ bulks. Considering that the contacted
area between MgB2 grains in the ex-situ bulks is limited by the porosity gaps [Figs. 3(b),
4(c)], it is considered that intergrain coupling is still insufficient compared with that in
the in-situ bulks.
Thus far the connectivity of ex-situ MgB2 is a trade-off balance between the
higher packing factor and the weaker intergrain coupling. Equation (2) predicts a high
connectivity of 30-40% for moderately sintered ex-situ MgB2 with P~75% owing to its
large P. Just a ~25% increase in P compared with that in in-situ MgB2 results in twice
or three times higher connectivity in ex-situ MgB2, if a sufficient arrangement of surface
contact between grains is achieved. Our results suggest that under controlled
atmosphere of Mg pressure, the solid-state self-sintering of MgB2 occurs and
significantly improves the intergrain coupling by heat treatment under an ambient
pressure. Given that homogeneous, single starting powder is favorable for the
fabrication of wires by the PIT method, sintered ex-situ MgB2 has advantages in both
connectivity and long-length wire fabrication. We believe the issues on the
microstructure of sintered ex-situ MgB2 bulks, such as large agglomerates and gaps
between grains, can reasonably be solved by the optimization of powder preparation and
heat treatment conditions in near future.
Finally we briefly mention the Jc of sintered ex-situ MgB2. What surprised us is
that the long heat treatment did not yield a significant increase in grain size. Indeed the
sintering promoted agglomerate formation; however, it just enhanced surface contact
and did not promote grain growth [Fig. 4(c)]. This is in strong contrast to that observed
in in-situ MgB2 bulks heated at high temperatures for a long period where grain growth
occurred and a marked deterioration in Jc was observed. We observed a higher Jc value
in the sintered ex-situ bulks than in the optimized in-situ bulks. Such critical current
properties in the relationship between the connectivity and microstructure of the
sintered ex-situ bulks will be reported in detail in a subsequent paper .
We studied the normal-state resistivity and microstructure of ex-situ MgB2
bulks synthesized with varied heating conditions under ambient pressure. The samples
heated at moderately high temperatures of ~900°C for a long period showed an
increased packing factor, a larger intergrain contact area, and a significantly decreased
resistivity, all of which indicate the solid-state self-sintering of MgB2. Consequently the
connectivity of the sintered ex-situ samples exceeded the typical connectivity range
5-15% of the in-situ samples. Our results show self-sintering can develop the superior
connectivity potential of ex-situ MgB2, though its intergrain coupling is not yet fulfilled,
to provide a strong possibility of realizing twice or even much higher connectivity in
optimally sintered ex-situ MgB2 than in in-situ MgB2.
This work was partially supported by Grants-in-Aid for Scientific Research
from the Japan Society for the Promotion of Science Nos. 23246110 and 22860019.
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Fig. 1. (a) Temperature dependence of resistivity for the ex-situ MgB2 bulks sintered at
different temperatures. Ex-situ bulk without heat treatment (as-pressed); in-situ- and
diffusion-processed bulks  are also shown for comparison. Figure 1(b) manifests
resistive transitions near Tc.
Fig. 2. Zero resistance temperature TR0 and connectivity K as a function of sintering
temperature for the ex-situ MgB2 bulks. All the samples were sintered for 24 h except
the samples without heat treatment and sintered for 48 h.
Fig. 3. Secondary electron images for the polished surface of MgB2 polycrystalline
bulks. (a) In-situ-processed MgB2 bulk from Mg and B, and (b) ex-situ-processed MgB2
bulk (sintered at 900°C for 24 h) from laboratory-made MgB2 powder.
Fig. 4. High-magnification secondary electron images for the polished surface of MgB2
polycrystal bulks. (a) Dense regions of the in-situ bulk, (b) ex-situ bulk without heat
treatment (as-pressed), and (c) ex-situ bulk sintered at 900°C for 24 h.
Fig. 5. Relationship between packing factor P and connectivity K for the in-situ
(including diffusion-processed)  and ex-situ MgB2 bulks.
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