A new MgB2 bulk ring fabrication technique for use in magnetic shielding or bench-top NMR systems

We report a new methodology in bulk MgB2 ring production for use in small-scale magnetic shielding or bench-top nuclear magnetic resonance systems. This process is a modified field-assisted sintering technique (mFAST) which enables direct formation of the rings without the need for machining or additives into the precursor powder. The shielding and trapped field capabilities of three mFAST MgB2 rings were determined using zero-field- and field-cooled magnetic experiments. Individual bulks trap magnetic fields up to 1.24 T at 20 K comparable to the highest published data for a ring sample. It is anticipated that for many applications, multiple rings will be stacked to form the required experimental structure. We find, for the three ring stack, a trapped field of 2.04 T and a maximum shielded field of 1.74 T at 20 K. The major factor limiting performance at low temperatures are flux jumps which cause rapid loss of the trapped field or shielding capability. Preliminary studies of magnetic field ramp rate dependence on flux jumps were conducted illustrating that even at very slow ramp rates (0.007 T min−1) they remain a significant issue. Despite this concern, we conclude that mFAST represents an exciting new fabrication methodology for bulk MgB2 rings.

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Introduction
Large-scale bulk samples are gaining traction as a new approach for the implementation of high temperature superconductors (HTSs). Two applications where bulks can a play a significant role are magnetic shielding and bench-top nuclear magnetic resonance (NMR) [1,2]. In these applications, the ideal bulk topology is a ring as it provides direct access to the geometric centre of the sample. However, accurate characterisation for each application requires slightly different techniques. In magnetic shielding, superconducting screening currents within the bulk act to magnetically protect an internal volume. Therefore, this behaviour is best characterised by measuring the magnetic field response at the bulk centre during the initial up-sweep of zero-field-cooled (ZFC) magnetisation. In contrast, for bulk-based NMR, it is the trapped magnetic field at zero applied field after fieldcooled (FC) magnetisations (B FC ) that is the figure of merit. In this case, the B FC works as a quasi-permanent magnet which can be used as the dc background magnetic field for NMR. For NMR, increasing the spatial homogeneity and temporal stability of B FC is also essential.
Due to the origin of the magnetic shielding and B FC , bulks in these applications effectively act as passive components without the need for external control. This potentially makes the systems simpler and smaller than conventional superconducting electromagnets. The lack of an external control structure means that superconducting joints can be removed from the system design. It is well established that HTS joints are a significant issue [3] which are particularly pertinent for NMR systems. In NMR, the magnetic field decay must in the range of parts per billion for real-world systems [4] which should be readily achievable with bulk superconductors [1,5].
To date, most bulk superconductor research has focussed on (RE)-Ba-Cu-O [(RE)BCO] cuprates due to the potential of trapped fields up to 17.6 T [6][7][8]. However, (RE)BCO bulks are difficult to manufacture, brittle and relatively dense (6.4 g cm −3 ) [9,10]. MgB 2 is considered a promising alternative for specific applications due to its range of physical properties. Not only is MgB 2 light (2.4 g cm −3 ) and mechanically robust [1], but the base materials are cheap. While the critical superconducting temperature (∼39 K) is lower than (RE)BCO it still lies within the capability of single-stage cryocoolers making system design uncomplicated. However, the main trade-off is the reduction in absolute performance. To date, a maximum B FC of 4.6 T in pure MgB 2 has been achieved [11]. Therefore, MgB 2 applications will be limited to low field applications particularly where weight is a significant issue [12].
In addition to these physical advantages, MgB 2 has a unique superconducting property which makes it ideal for bulks. Due to MgB 2 large coherence lengths (in the ab-plane: 39 ± 11 nm, and 35 ± 10 nm in the c-plane [13]) even polycrystalline samples can act as a continuous bulk superconductor. Not only does this make bulk synthesis relatively straightforward but it also eradicates the growth sector boundary related inhomogeneous field distribution observed in (RE)BCO bulks [9].
To date, two distinct synthesis methodologies are used for MgB 2 bulks: field-assisted sintering technique (FAST) [14,15] and reactive liquid Mg infiltration [16]. While the size of infiltration growth samples is only limited by the reaction chamber, FAST samples have been shown to produce the highest J C and therefore have the potential to shield or trap greater fields [2]. However generating large ring bulks with FAST is not trivial. FAST requires high temperature and pressure which places the bulk under significant stresses during the manufacturing process [17]. In the existing literature, FAST has only been used to directly fabricate disks or solid cylinders of MgB 2 which cannot be simply used for magnetic shielding or NMR systems. However, machining is complicated by the mechanical strength of pure MgB 2 which can lead to damage of the bulk structure during this process. To counteract this, Gozzelino et al [15] have developed a technique where pure MgB 2 powder is mixed with hexagonal boron nitride before the FAST process. This reduces the strength making machining possible but potentially reducing the superconducting properties making this process non-ideal. We note that Naito et al [18] also successfully machined a ring of comparable size from a hot isostatic pressed bulk although the reproducibility of this process was not discussed. In this work, we outline a modified FAST (mFAST) process which achieves the goal of direct fabrication of MgB 2 bulk rings without machining or precursor additives and investigate the superconducting properties using magnetisation experiments.

Ring manufacturing-mFAST
A two-stage fabrication approach is necessary to generate rings using mFAST. Initially, disk samples are formed using a conventional ex-situ FAST approach [19]. Commercial MgB 2 powder was compressed into a graphite mould and placed into Dr Fritsch DSP507 FAST machine (https://dr-fritsch.de/). Through an iterative study, the optimum conditions for generating dense bulks was established. Following our previous study [14], we find a sintering time of 5 min with a pressure of 50 MPa and temperature of 1150 • C produced samples with the highest trapped field and a measured density of 96%. These re-usable disks play an essential role in the ring formation by operating as the internal structures generating the inner ring radius.
To generate ring samples, a bespoke mould structure was developed consisting of graphite outer former, ring stamp and half-shells with a unique internal pin structure, as shown in figures 1(a) and (b). The internal pin structure must be formed using the pre-pressed MgB 2 bulk disk sandwiched between two graphite pins, as displayed in figure 1(c). All surfaces were covered with graphite paper throughout this process. This construction ensures that the thermal contraction rates of the formed ring and internal pin structure are matched, significantly minimising temperature induced stresses. In combination with close control of the cooling profile, this experimental structure maintains the structural stability of the ring throughout the mFAST procedure. If a uniform graphite pin is utilised,  the mFAST methodology did not reproducibly generate bulk rings of the size displayed in figure 2. Instead, after the sintering process, the rings were found to be fractured.
This process generated three MgB 2 rings with dimensions of 37 mm outer diameter, 21 mm inner diameter and 9.3 mm thickness. In figure 2, the samples considered in this work are displayed to scale with existing literature MgB 2 rings. The physical size of the samples lie in between the existing machinable FAST samples discussed by Gozzelino et al [2,15] and the larger Namba et al [20] samples formed by infiltration growth. However, they are a similar size to the machined samples of Naito et al [18].

Microstructural characterization
X-ray diffraction (XRD) measurements were performed using a PANalytical Empyrean diffractometer with CuKα radiation (λ = 0:154 nm) at 40 kV and 40 mA. The weight fraction of the different phases present in the samples were estimated from the XRD patterns using Rietveld refinement (PANalytical HighScore Plus software). Scanning electron microscopy (SEM) analysis was carried out using a Zeiss Merlin SEM with an Oxford Instruments 150 mm 2 XMax EDX detector.

Magnetisation experiments
Magnetic measurements were performed using a 12 T large bore magnet system (ICEoxford, UK). The samples were measured as individual rings and as a stack of three rings. In both cases, the rings were coated with a thin layer of Apiezon-N cryogenic grease (M&I Materials Ltd) and inserted into a tufnol holder. The structure was then clamped onto a copper mounting plate, as shown in figure 1(d). The temperature was measured using an in-built Cernox thermometer embedded in the copper mounting plate. The entire measurement apparatus was installed in a helium-flow variable temperature insert allowing precise temperature control. An experimentally calibrated hall sensor (Lakeshore HGT-2101) was positioned at the ring or stack centre aligned to measure the field along the longitudinal axis. Both the FC and ZFC behaviours were measured at a range of temperatures (5 K, 10 K, 15 K, 20 K, 25 K, 30 K) with two magnetic field ramp rates (0.025 T min −1 and 0.007 T min −1 ).
The magnetic shielding is characterised by the shielding ratio (S R ) [2] during the initial upward positive field sweep: where µ 0 H (T) is the applied magnetic field. We assign S R < 0.01 (S R (99%)) as representing complete shielding of the external magnetic field. Figure 3 shows the microstructure of a typical ring bulk sample. At low magnification, the sample shows a wellconnected microstructure containing a small volume fraction of pores (black regions) illustrating the high quality of the produced samples. At higher magnification (figure 3(b)) four different contrast levels can be observed. These correspond to the solid phases of MgB 2 (light grey), MgB 4 (dark grey) and MgO (white), and porosity (black). This phase assignation has been confirmed by energy dispersive X-ray elemental maps presented in figure 3(c). This data shows that the MgB 2 ring consists of a connected matrix of MgB 2 phase with very fine round MgO particles (<1 µm) and individual larger particles of MgB 4 (2-10 µm) randomly distributed over the matrix. The sample shows a fairly dense microstructure with small individual pores which are not expected to interrupt a continuous path for supercurrent. The volume fraction of MgO in the sample was estimated by image contrast analysis to be 4.3 vol.% (∼6.5 wt.%) consistent with 6 wt.% calculated by XRD and with existing non-ring FAST samples [14]. Further details can be found in the related supplementary material.

Results
In figure 4(a), the B Z (T) response for the initial positive magnetic field down sweep (5 T-0 T) after FC at 10 K, 20 K and 30 K for the stack is displayed. The 20 K data for a single ring is shown for comparison. Firstly, the B FC of the mFAST single rings is comparable to ring samples formed requiring additional machining [15,18]. Secondly, the stacking of three bulks increases B FC from 1.24 T to 2.04 T-a ∼65% increase in B FC . While this value is less than the infiltration growth Namba et al [20] sample (2.2 T at 20 K) the disparity stems from the greater physical size of the Namba sample (see figure 2). The generation of larger rings should enable larger B FC to be achieved. While this data illustrates the potential of mFAST tubes further analysis exploring the uniformity of the generated magnetic field within the bore will be essential for NMR applications.
One significant issue are flux jumps which limit both the observed B FC and shielding capability at temperatures below 25 K. Firstly, it should be noted that while flux jumps affect both the ZFC and FC measurements (which correlate to S R (99%) and B FC respectively), the ZFC experiments are more susceptible. To illustrate this variation, consider the dashed lines in figures 4(a) and (c) which display the 20 K response for FC and ZFC during the initial upward field ramp using a 0.025 T min −1 ramp rate respectively. In the FC scenario ( figure 4(a)) the stack is resilient to flux jumps. Conversely, in ZFC a flux jump is observed. Indeed, flux jumps are observed at all temperatures below 25 K in the ZFC scenario (dashed line, figure 4(d)) while they are only observed at 15 K and below in FC. Due to flux jumps, the maximum shielded field using S R (99%) was observed at 15 K (2.05 T). This value is comparable to the best performance in the literature [12,15].
In figure 4(d), we consider the effect of magnetic ramp rate on the flux jump behaviour in the ZFC scenario. Lowering the ramp rate increases the flux jump resilience. For instance, with a 0.007 T min −1 ramp rate at 25 K no flux jumps are observed unlike at 0.025 T min −1 . However, a 0.007 T min −1 ramp rate remains insufficient to stop flux jumps below 25 K. This flux jump sensitivity may act as a significant limiting factor for MgB 2 based shielding applications.
In figure 5(a), the B FC and S R (99%) values at all temperature using a 0.025 T min −1 magnetic ramp rate are shown. If flux jumps do not significantly alter the performance, S R (99%) is around 85% of B FC . Therefore, it is essential that the shielding ability is not directly inferred from trapped field measurements but is characterised using a ZFC methodology. To ascertain the non-flux jump performance, extrapolated values for B FC were calculated using a non-linear curve fitting technique from the high field functional form. This is shown graphically by the black half squares in figure 4(a). Using this extrapolation, a B FC of 3.7 T would be achieved at 5 K without flux jumps. ) using two post-magnetisation temperature procedures. In one case, the stack remains at 20 K; in the other, the stack is cooled to 6 K after the magnetic down sweep. The decay rate after 10 000 s drops from 50 ppb h −1 in the consistent temperature procedure to 0.2 ppb h −1 when the stack was cooled to 6 K.
For NMR applications, it is vital that the B FC temporal stability is maximised to enable long term use without continual remagnetisation. Recent work by Takahashi et al [1] illustrated that cooling after the magnetisation significantly improves the magnetic field persistence. However, the B FC value explored in that work was substantially smaller than the absolute performance of their sample, potentially leading to an overestimation of the true persistence. Therefore, to quantify the improvement of post-magnetisation cooling, we evaluated the stability for two cases: no post-magnetisation cooling (sample remains at 20 K) and cooling of the stack to 6 K after optimal magnetisation (B FC = 2.04 T). We find that without cooling the field decay was 50 ppb h −1 , as shown in figure 5(b).
For post-magnetisation cooling, the decay rate reduces by two orders of magnitude to 0.2 ppb h −1 . Illustrating that excellent persistence can be achieved even near optimal B FC .

Conclusions
We have investigated the trapped field and shielding properties of MgB 2 rings using two magnetisation procedures (FC and ZFC) as a function of temperature, applied magnetic field magnitude and ramp rate. The rings were directly formed without machining using modified FAST. In modified FAST, a unique internal pin structure, using a pre-formed MgB 2 bulk, is used to generate the internal ring radius. This process reproducibly generates ring bulks with dimensions of 37 mm outer diameter, 21 mm inner diameter and 9.3 mm thickness. The individual rings demonstrate a 20 K trapped field of 1.24 T which increases to 2.04 T for a stack of three rings at 20 K. Therefore, this new fabrication methodology demonstrates significant promise for producing high quality ring bulks with properties beyond the existing literature data.
Flux jumps play a significant role in limiting the performance of the stack. This is particularly acute in zero-fieldcooling and, therefore, shielding scenarios. At temperatures below 30 K, flux jumps are observed in the ZFC data using a 0.025 T min −1 applied field ramp rate. In comparison, flux jumps are only at observed at temperatures below 15 K in the FC data. These flux jumps limit the observed shielding field to the 2.05 T seen at 15 K. The flux jump stability can be improved using a slower ramp rate, however, the sensitivity to flux jumps must be considered a significant hindrance for magnetic shielding applications.
Finally, the stack trapped field temporal stability was explored for FC magnetisation at 20 K using two different post-magnetisation procedures. If the stack is cooled to 6 K after magnetisation, the field decay decreases to 0.2 ppb h −1 representing 250× improvement in trapped field persistence compared to no cooling after magnetisation. Further work exploring the homogeneity of the trapped field and methodologies for the limiting the effect of flux jumps will be essential for real-world applications.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: 10.17863/CAM.78758. The University of Cambridge would like to acknowledge Henry Royce Institute Equipment Grant: EP/P024947/1.