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Potential ability of 3 T-class trapped field on MgB2 bulk surface synthesized by the infiltrationcapsule method

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2016 Supercond. Sci. Technol. 29 115003(http://iopscience.iop.org/0953-2048/29/11/115003)
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Superconductor Science and Technology
Supercond. Sci. Technol. 29 (2016) 115003 (6pp)

doi:10.1088/0953-2048/29/11/115003

Potential ability of 3 T-class trapped ﬁeld on
MgB2 bulk surface synthesized by theinﬁltration-capsule method
Tomoyuki Naito, Arata Ogino and Hiroyuki Fujishiro
Faculty of Science and Engineering, Iwate University, Morioka 020-8551, Japan
E-mail: tnaito@iwate-u.ac.jp
Received 13 May 2016, revised 11 July 2016
Accepted for publication 3 August 2016
Published 26 September 2016
Abstract

We successfully synthesized a dense (∼90%-ﬁlled) MgB2 bulk with no residual Mg via an
inﬁltration process by overcoming the problems in this process such as the expansion of a B
precursor disk under a liquid Mg inﬁltration and the residuals of unreacted Mg in the bulk using
a specially designed capsule. As a result, we have achieved a record-high trapped ﬁeld to date,
BT , of 2.4 T at the center of the bulk surface at the lowest temperature of 15.9 K among theinﬁltration-processed MgB2 bulks. The trapped-ﬁelds simulated for a model with theexperimental Jc (m0 H ) characteristics well reproduced the experimental BT ’s and gave a reliable
estimated BT below 15.9 K. The extrapolation of the experimental and simulated BT curve
reached 3 T at 4.2 K. The critical current densities, Jc (m0 H )’s, at 20 K were 1.8×105 Acm−2
under the self-ﬁeld and 4.5×103 Acm−2 under the magnetic-ﬁeld of m0 H = 3 T. The
connectivity, K, of 16% of the present bulk was comparable with that of the ∼50%-ﬁlled MgB2
bulk. The high BT with low K and the microstructure of the present bulk suggested that the highand low-Jc regions coexisted because of the wide variation of the MgB2 grain-size.
Keywords: MgB2, inﬁltration process, trapped ﬁeld, bulk magnet(Some ﬁgures may appear in colour only in the online journal)pressure by two groups [8, 9], just after the discoveryof the superconductivity in MgB2. Continuous numerous
studies [10–18] conﬁrmed the Tesla-order MgB2 bulk
magnets, in which the BT has been enhanced up to 4–5 Tesla
to date by the improvement of the fabrication process and/or
the introduction of the pinning centers [14–16]. The recordhigh BT of 5.4 T at 12 K was realized for the MgB2 bulk
(20 mm in diameter and 8 mm in thickness; 20 mmf×8 mmt) fabricated by an ex-situ uniaxially HP method usingball-milled nanometric MgB2 powder [14]. The in-situ HIPtechnique also produced a strong MgB2 bulk magnet(26 mmf×7 mmt) trapping 2.5 T at 12.7 K, which wasincreased by 1.6 times from 1.6 T at the same temperature forthe 50%-ﬁlled MgB2 bulk (30 mmf×9 mmt) [13]. Moreover, the Ti-doping offered the BT of 3.6 T at 13.4 K at thesurface of a single HIP-processed bulk and 4.6 T at 14.1 K at
the center of stacked bulk pair [16]. A homogeneous conicalBT proﬁle [10, 15] due to the polycrystalline form and1. Introduction
MgB2 superconducting bulks and wires have been intensively
studied to use in a practical superconducting apparatus
because of the speciﬁc advantages of well-connected grains
for supercurrent ﬂowing [1, 2] and a relatively high criticaltemperature, Tc , of 39K [3]. However, a low ﬁlling factor of
about 50%–75% of the ideal density and a large degradationof Jc under magnetic-ﬁelds are obstacles to producing a strong
bulk magnet trapping over 10 T or to replacing the conventional low-Tc materials such as NbTi and Nb3Sn by MgB2 forwire applications. High-pressure synthesis including a hot
isostatic pressing (HIP) [3, 4], hot pressing (HP) [5], spark
plasma sintering (SPS) [6, 7], and so on offers an over 90%ﬁlled MgB2 with enhanced Jc due to the increase of thesupercurrent path and the number density of the grainboundaries as a dominant pinning center. The polycrystalline
MgB2 bulks trapping 1–2 T were produced under high0953-2048/16/115003+06$33.00

1© 2016 IOP Publishing Ltd Printed in the UK

Supercond. Sci. Technol. 29 (2016) 115003

T Naito et ala highly stable BT [15, 16] due to the small vortex-creep
phenomenon could compensate a shortcoming of relatively
low BT of MgB2 bulk compared to that of a RE-Ba-Cu-O bulk
[19–21], and therefore MgB2 bulk magnets are good candidates for a practical superconducting application which
requires a highly homogenized and stabilized magnetic ﬁeld.
In contrast to high-pressure synthesis, highly dense
MgB2 can also be prepared by an inﬁltration (diffusion)
process above the melting point of Mg (Tm.p.=650 °C)
without external physical pressure [22, 23]. In this process,the liquid Mg initially inﬁltrates into a B preform via thecapillary effect, which leads to the expansion of the B preform, reacts with B to form MgB2, shrinking about 25% involume. The change in volume and the uncontrollable
capillary effect result in an inhomogeneous bulk with cracks
and a large amount of unreacted Mg as a channel- and/or
thread-like shape, as reported previously [18, 22]. Several BT
values have been reported for the inﬁltration processed (IP)
MgB2 bulks; the MgB2 bulk (55 mmf×10 mmt) fabricatedby a reactive liquid-Mg inﬁltration (Mg-RLI) method
offered a BT of 1.98 T at 19.4 K [17]. This BT was notnecessarily larger than that of a smaller HIP MgB2 bulk
(26 mmf×7 mmt) [13], although the ﬁlling factor( f 90%) and Jc (m0 H ) of both bulks were nearly identical.
The inhomogeneity in the microstructure of the Mg-RLI bulk
probably degraded the BT , which was supported by the nonuniform BT distribution obtained by pulsed-ﬁeld magnetization (PFM) for the same bulk [24]; the vortex pinning properties in PFM is known to be quite sensitive to theinhomogeneity of the superconductivity in the bulk. Recently,
a homogeneous MgB2 bulk (32 mmf×6 mmt) with ﬁnely
dispersed Mg particles was successfully obtained by a modiﬁed precursor inﬁltration and growth (MPIG) method [18];the highest BT of 2.1 T at 5 K was achieved, which corresponded to that at 20 K for the smaller HIP bulk [13]. To
enhance the trapped ﬁeld properties of the IP MgB2 bulk ashigh as that of high-pressure synthesized bulks, we have toresolve the problems of the volume expansion of the B preform at the initial process and of the residuals of unreacted
Mg in the MgB2 bulk. In the present paper, we report on thetrapped magnetic-ﬁeld properties of a highly dense andhomogeneous MgB2 bulk prepared by the inﬁltration method
using a home-made capsule and discuss the potential abilityof the IP MgB2 bulk as a quasi-permanent magnet.

Figure 1. Schematic image of the capsule for the inﬁltration process.

Chemical Laboratory Co., Ltd) and crystalline B powder(99% in purity, 45 μm in grain size, Kojundo Chemical
Laboratory Co., Ltd) were weighed with Mg:B=1.6:2.0
in molar ratio and pelletized individually under a uniaxialpressure of about 30 MPa in air; the excess Mg was expected
to compensate for the lack of liquid Mg source. Each Mg andB precursor was set individually in the hole of the stainlesssteel container, and then sealed with the soft-iron gasket using
the bolts and nuts under Ar atmosphere in a glove box. The
closed capsule was ﬁred at 900 °C for 9 h in a box furnace andcooled down to room temperature by furnace cooling. Abovethe melting temperature of Mg, 650 °C, the liquid Mg started
to inﬁltrate into the B pellet through the holes of the gasket,
and then MgB2 was created by a liquid–solid reaction. Assynthesized MgB2 bulk was machined into a disk with 30 mm
in diameter and 6.6 mm in thickness, as shown in ﬁgure 2, in
which a large amount of the residual unreacted Mg on thebulk surface was fully removed by polishing. Left and right
pictures, respectively, are the top surface, which was facing
the Mg pellet, and the bottom one (opposite side) of the MgB2
bulk. The soft-iron gasket could not fully suppress the
expansion of the B pellet, resulting in the creation of cracks
less than 1 mm in depth on the top surface.

2.2. Method of measurements

The MgB2 bulk was magnetized at 15.9 K by ﬁeld-cooledmagnetization under a magnetic ﬁled of m0 H = 5 Tesla. A
trapped ﬁeld on the top surface of the bulk was measured by acryogenic Hall probe (HP-VVP, AREPOC s.r.o.) with elevating temperature at a rate of 0.1 K/min. The temperature of
the bulk was monitored by a Cernox thermometer which was
adhered on the bulk surface by a GE7031 varnish. Magnetization, M, was measured as functions of temperature andmagnetic-ﬁeld using some small pieces cut from the bulk by acommercial SQUID magnetometer (MPMS-XL, Quantum
Design Inc.). Magnetic-ﬁeld dependence of the critical current
density, Jc (m0 H ), was estimated from the magnetic hysteresis
curve, M (m0 H ), using the extended Bean model [25, 26],
Jc = 20DM a (1 - a 3b ), where ΔM is the width of thehysteresis, and a and b (a<b) are the cross-sectional
dimensions of the sample perpendicular to the appliedmagnetic-ﬁeld. Electrical resistivity, ρ, was measured by a

2. Experimental Procedure
2.1. Fabrication of MgB2 bulk via an infiltration process

A MgB2 bulk was fabricated by an in-situ inﬁltration method
in a closed home-made capsule. As schematically shown inﬁgure 1, the capsule consisted of a pair of stainless steel (SS)containers with holes (30 mm in diameter and 9 mm in depth)
and a soft-iron gasket (1.6 mm in thickness) with 58 throughholes (2 mm in diameter); the sealing mechanism was thesame as that of a commercial CF ﬂange and gasket. Mg
powder (99% in purity, 180 μm in grain size, Kojundo2Supercond. Sci. Technol. 29 (2016) 115003

T Naito et al

Figure 2. Photographs of the top (left) and bottom (right) surfaces of the inﬁltration-processed MgB2 bulk after machining.

standard four-probe method with a typical current density of
1 Acm−2. Microstructure of the bulk surface was observed
by a scanning electron microscope (SEM).
2.3. Numerical simulation procedure

Trapped ﬁelds of the present bulk were estimated for 10, 20
and 30 K from the numerically simulated electromagnetic
ﬁelds using a commercial ﬁnite-element-method (FEM)
software, Photo-Eddy (PHOTON., Ltd., Japan). A small
temperature rise of about 0.1 K on the bulk surface during the
FCM allowed the simulation under a constant temperature. A
simulation model with two-dimensional axisymmetric coordinates was constructed based on the experimental set-up,
which was described elsewhere [27]. The power-n value
model, E=Ec( J/Jc)n, described the nonlinear E − J characteristics, where E the electric ﬁeld, Ec=1 μVm−1 thecriterion and n=100 [27]. The experimental Jc (m0 H ) was
estimated by the following relation,3⎧⎧⎛ m H ⎞b ⎫⎛ T ⎞2 ⎫ 2⎪⎪
Jc (m 0 H ) = a ⎨1 - ⎜ ⎟ ⎬ exp ⎨.
⎜ 0 ⎟ ⎬⎪⎪⎝ Tc ⎠ ⎭⎩⎩ ⎝ m 0 H0 ⎠ ⎭
⎪

⎪

⎪

⎪

Figure 3. X-ray diffraction patterns of the top and bottom surfaces of
the inﬁltration-processed MgB2 bulk.

(1 )and bottom surfaces are nearly comparable. Giunchi et alargued that Mg2B25 was created at the initial stage of theinﬁltration process and did not prevent the supercurrent
ﬂowing [28]. No diffraction peaks of Mg means no residual
unreacted Mg in the present bulk. The inset of ﬁgure 4 shows
the temperature dependence of the normalized magnetization
for three positions (top, middle, bottom) of the bulk, which
was measured at m0 H = 0.4 mT after zero-ﬁeld cooling.
Three pieces were cut from the top and bottom surfaces andthe center of the bulk (middle), respectively. Almost the same
critical temperatures of about 38.6 K were observed; Tc wasdeﬁned at the mid-point of the transition. The ﬁlling factors,fʼs, evaluated by the Archimedes method, was typicallyHere, the used parameters were α(=Jc at 0 K), μ0H0(characteristic magnetic-ﬁeld) and β.

3. Results and discussion
Figure 3 shows the x-ray diffraction patterns taken at room
temperature using the Cu-Kα radiation for both the top andbottom surfaces of the bulk. The dominant MgB2 phase witha small amount of impurity peaks of Mg2B25 was conﬁrmed,
in which the amount of Mg2B25 impurity phase at both the top3Supercond. Sci. Technol. 29 (2016) 115003

T Naito et al

Figure 5. Magnetic-ﬁeld dependence of the critical current density,

Jc (m0 H ), at 10, 20, 30 K for the inﬁltration-processed MgB2 bulk.
The thick solid lines are the Jc (m0 H )’s estimated by the equation (1)with the appropriate parameters (see text), which were used to obtainthe simulated BT in ﬁgure 4. The dotted lines are the Jc (m0 H ) of the
HIP processed MgB2 bulk (HIP#38 [16]).

Figure 4. Temperature dependence of the trapped magnetic-ﬁeld at

the top-surface of the inﬁltration-processed MgB2 bulk. Open circles
and closed squares are the experimental and simulated (see text) BT
values. The thick solid line is a ﬁtting curve as
BT (T ) = B0 {1 - (T Tc )2 }m with the ﬁtting parameters of
B0 = 3.01 T and m = 1.25. The thick dashed-dotted line is the BT (T )of the HIP processed MgB2 bulk (HIP#38 [16]). The inset shows
the temperature dependence of the normalized magnetization at
m0 H = 0.4 mT after zero-ﬁeld cooling for the indicated threepositions of inﬁltration-processed MgB2 bulk.

with that of the HIP#38 bulk, except for the low ﬁelds. The
irreversibility ﬁelds, m0 Hirr ’s, of 4.5 T at 20 K and of 1.8 T at
30 K obviouslyexceeds those of the HIP#38 bulk, where them0 Hirr was deﬁned as the magnetic-ﬁeld at Jc =10 Acm−2.
The Jc (m0 H ) behaviors support the excellent BT characteristics of the present bulk. As shown in the main panel ofﬁgure 4, the BT ’s at 20 and 30 K simulated using the experimental Jc (m0 H ) characteristics well reproduced the experimental BT ’s, and the simulated BT was 2.7 T at 10 K. The
Jc (m0 H )’s used in the simulation are depicted in ﬁgure 5,
which were estimated using the following parameters;α=4.0×105 Acm−2, Tc =39.6 Kand the combinationsof μ0H0 and β were 1.3 T and 1.2 for 10 K, 1.1 T and 1.4 for
20 K and 0.5 T and 1.2 for 30 K. The simulation results
indicate strongly the good agreement between the microscopic Jc of the millimeter-size specimen and macroscopic Jcof the centimeter-size bulk, and then the homogeneous
structure and composition of the present bulk in these scales.
The reproducibility of BT in the simulation using the experimental Jc (m0 H ) were reported previously for the other MgB2
bulks [27, 29]. Assuming the relationship between the trapped
ﬁeld and irreversibility ﬁeld, m0 Hirr µ {1 - (T Tc )2 }m [30],both experimental and simulated BT (T ) was well ﬁtted by
BT (T ) = B0 {1 - (T Tc )2 }m with a BT at 0 K, B0 = 3.01 T
and a characteristic exponent, m = 1.25, as shown in ﬁgure 4.
The estimated BT (T ) of 3 T at 4.2 K conﬁrms evidently thepotential ability of the present IP bulk trapping 3 T classmagnetic-ﬁeld on the bulk surface.
Figure 6 shows the temperature dependence of theresistivity, r (T ), for the present bulk. The r (T ) of the
HIP#38 bulk is also shown as a reference [31]. The zeroresistivity transition temperature of 38.6 K, deﬁned at the
mid-point of the transition, agreed well with that of themagnetic transition. More than ﬁve times larger r (T ) is
observed for the present IP bulk compared to the HIP#38∼90%. These results demonstrate that a highly dense MgB2
bulk with homogeneous composition and superconductivity
was obtained.
The main panel of ﬁgure 4 shows the trapped magneticﬁeld, as a function of temperature, BT (T ), for the present IP
bulk. The BT (T ) curve of the HIP MgB2 bulk( f∼95%,
38 mmf×7 mmt), named as HIP#38, is also shown forcomparison [16]. The BT of 2.4 T was achieved at 15.9 K and
BT decreased monotonically with increasing temperature dueto the Jc -decrease and reached zero at 39.6 K due to thetemperature-gradient in the bulk. The BT (T ) value of thepresent IP bulk was comparable to that of the HIP#38 bulk,
regardless of the 20% smaller diameter and smaller f of
∼90%. Moreover, comparing at the same temperature of
19.4 K, the BT of 2.12 T for the present IP bulk
(30 mmf×6.6 mmt) evidently breaks the record-high BT of
1.98 T for the Mg-RLI bulk (55 mmf×10 mmt) [17]. The
home-made capsule with soft-iron gasket almost suppressed
the expansion of the bulk along both the radial and thickness
directions, resulting in the highest BT among the IP MgB2
bulks to date.
Figure 5 shows the magnetic-ﬁeld dependence of thecritical current density, Jc (m0 H ), at T = 10, 20 and 30 K forthe present bulk. The Jc (m0 H )’s of the HIP#38 bulk at thesame temperatures are also depicted as a reference [16]. All
the Jc (m0 H ) curves decreased monotonically with increasing
magnetic-ﬁeld, which is commonly observed in MgB2. The
magnitude of Jc (m0 H ) of the present IP bulk was comparable
4

Supercond. Sci. Technol. 29 (2016) 115003

T Naito et alprobably originated from the similar distribution of grain sizeof the as-purchased B powder, revealed by the SEM image(not shown here), as reported previously [34]. These grains do
not seem to connect well with each other, which is qualitatively consistent with the estimated small K value of 16% andthe high resistivity; in particular, the island-shaped grains
prevent the supercurrent ﬂowing. To explain the high trapped
ﬁeld (high-Jc ) with low connectivity for the present IP bulk,
we suggest the possibility of the coexistence of high- andlow-Jc regions owing to the different grain sizes. A MgB2
wire fabricated by the internal Mg diffusion (IMD) method,which is a kind of inﬁltration process, is well known to offer ahigh-Jc of about 105 Acm−2 under 3 T at 20 K [35]. This Jc isabout two orders of magnitude larger than that of the presentbulk at the same condition. If the similar high-Jc MgB2
regions exist locally in the present IP bulk, the high-BT with
low-K can be explained. A direct observation of the supercurrent proﬁles in the bulk by a scanning Hall probe microscopy [36] probably conﬁrms this scenario.

Figure 6. Temperature dependence of the resistivity for theinﬁltration-processed MgB2 bulk. The dotted line is the ρ(T) of the
HIP processed MgB2 bulk (HIP#38 [31]).

4. Summary
In summary, we have studied the trapped magnetic-ﬁeld, BT ,properties of a MgB2 bulk fabricated by the inﬁltration
method in a home-made capsule. The highly dense MgB2
bulk free from the residual unreacted Mg (ﬁlling factor, f, of∼90%, 30 mm in diameter and 6.6 mm in thickness) was
successfully obtained. This bulk offered a record-high BT of
2.4 T at 15.9 K among the inﬁltration processed MgB2 bulks,
which was comparable with those of the high-pressure synthesized bulks. The critical current densities at 20 K wereabout
1.8×105 Acm−2
inthe
self-ﬁeld
and3
4.5×10 Acm−2 under m0 H = 3 T. The irreversibility ﬁeld
was 4.5 T at 20 K. A good consistency was found for theexperimental and simulated BT ’s, and the extrapolation ofwhich reached 3 T at 4.2 K, suggesting the potential ability ofbulk trapping 3 T on the bulk surface. The effective crosssectional ratio, K, proposed by Rowell, for the supercurrent
path was estimated to be as low as 16%, which was probably
caused by the island-shaped large MgB2 grains a few tens of
microns in size. The inconsistency among the high BT , high Jc
and low K remains an unsolved problem.

Figure 7. SEM images with the same scales of the top surfaces of theinﬁltration-processed (main panel) and of the HIP-processed (inset;
HIP#38 [31]) MgB2 bulks.

bulk, although there is a small difference in the ﬁlling factor,
less than 10%, between them. We evaluated the effective
cross-section for the supercurrent-path in the bulk by estimating the connectivity, K, using the Rowell’s relation,
K = (Drs Drp ) ´ 100 (%) [32]. Here, Δρs and Δρp are thedifference in the resistivity between 300 K and 40 K for the
single crystal and the polycrystal, respectively. In this relation, the connectivity was assumed to be 100% for the single
crystal, and we used Δρs = 6.32μΩcm [33]. The K value
was estimated to be 16%, which is rather smaller than 75% of
the HIP#38 bulk [31]. The main panel of ﬁgure 7 shows atypical SEM image of the top surface of the present bulk; notethat almost the same microstructure was also observed at the
middle and bottom positions. In contrast to the microstructure
consisting of nanometric grains for the HIP#38 bulk [31],shown in the inset of ﬁgure 7, the large island-shaped MgB2
grains with a few tens of microns in size and the assembly ofsmall grains with micron and sub-micron in size wereobserved in the present bulk. It is noteworthy that no
unreacted Mg particle was observed, which is consistent with
the XRD result. The wide variation of the MgB2 grain-size

Acknowledgments
This work was partly supported by JSPS KAKENHI Grant
Numbers 15K04718, 15K04646.

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