Correlation between microstructure and superconducting properties of MgB2 bulk samples with Mg addition and Mg/hBN co-additions

The microstructure of polycrystalline MgB2 has a strong influence on the current carrying ability, with grain boundaries and non-superconducting nanoparticles acting as good flux pinning centres which improve the local (intrinsic) critical current density (J c) of the material, whereas porosity and poor connectivity between grains or particles adversely affect macroscopic current transport. Previous studies have found that hexagonal boron nitride (hBN) doping improves intrinsic J c by introducing nanoscale flux pinning centres, and Mg doping improves extrinsic J c by liquid-assisted sintering. Here we investigate the effect of co-doping with 5 wt.% Mg and 1 wt.% hBN with the aim of combining the improved intrinsic and extrinsic properties in bulk MgB2 samples fabricated using field assisted sintering. Additionally, the influence of ball milling and processing temperatures on MgB2 samples with only Mg additions is reported. By correlating microstructure with superconducting properties, we show that the presence of Mg liquid during processing of Mg-doped samples accelerates the reaction between BN and MgB2, forming an impurity phase, MgNB9, the presence of which is detrimental to superconducting performance. Nevertheless, we have achieved a considerable improvement in performance of samples doped only with Mg by increasing the sintering temperature.


Introduction
MgB 2 bulk samples are promising superconducting materials for compact or portable medium-field magnet applications * Author to whom any correspondence should be addressed.
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because MgB 2 has a higher critical temperature (T c = 39 K) than any other conventional low temperature superconductors at ambient pressure, and unlike high temperature cuprate superconductors, does not suffer from grain boundaries acting as weak links [1]. This means that polycrystalline bulk MgB 2 samples can be manufactured by simple, scalable and cheap powder processing techniques. Many methods have been used to improve the critical current density (J c ) at high fields in MgB 2 bulks in order to maximise the magnetic field that can be trapped. The effects can be divided, using the terminology of Collings et al [2], into intrinsic factors which affect the superconductivity within well-connected, dense particles (e.g. H c2 by impurity scattering and local J c by flux pinning), and extrinsic factors such as density, fraction of the superconducting phase and the cleanliness of the boundaries that influence the macroscopic J c that can flow through the whole sample.
It is generally agreed that the dominant pinning mechanism in MgB 2 is grain boundary pinning [1][2][3]. High-energy ball milling can effectively refine the MgB 2 powder particles, resulting in sintered material with a higher density of grain boundaries that contribute to vortex pinning, thus enhancing intrinsic J c values [4][5][6]. Chemical doping is another popular method for increasing J c . A large variety of dopants have been investigated, including carbon and carbides [7][8][9][10][11], rare earth oxides [12][13][14] and metals [15][16][17][18]. It is widely accepted that localized lattice strains caused by carbon substitution for boron in the MgB 2 lattice increase H c2 and intrinsic J c at the cost of a significant decrease in T c [19,20]. Rare earth oxide nanoparticle additions with a size comparable to the coherence length of MgB 2 (∼10 nm) are found to be effective in strengthening flux pinning and enhancing intrinsic J c [13,21,22]. The addition of low melting point metals can lower the sintering temperature and improve the extrinsic connectivity of the MgB 2 particles by encouraging liquid phase sintering [15,16,23,24]. Specifically, we have shown previously that Mg additions to commercial MgB 2 powders could enhance J c over the whole range of fields in ex-situ samples prepared at 900 • C by Field Assisted Sintering Technology (FAST) [25]. However, even with 10 wt.% Mg addition, the MgB 2 microstructure is not fully dense, which suggests that there is the opportunity to further improve the J c values.
Even though the effects of many different kinds of dopants have been reported, there is a lack of consistency in the literature on the specific microstructural changes arising from the choice of different starting powders and processing conditions. Interpretation of the effects of composition and processing on the superconducting properties of bulk samples requires analysis of the combination of intrinsic and extrinsic factors and is often hampered by a lack of detailed microstructural characterization. For example, we have recently reported that adding hexagonal boron nitride (hBN) nanoparticles can improve J c by adding effective pinning centres [26], but hBN doping was also found to have a detrimental effect on the connectivity of the MgB 2 particles, with chemical reactions leading to the generation of impurity phases and porosity. Therefore, one of our aims in this work is to investigate whether addition of excess Mg can act as a sintering aid in hBN-doped MgB 2 (section 3.1), so we can benefit from the intrinsic J c enhancement due to hBN-derived pinning centres without compromising the connectivity of the samples. For comparison, we also prepared ex-situ samples by FAST with only Mg additions (section 3.2). Detailed microstructural characterisation of both groups of MgB 2 samples processed at different temperatures was performed and correlated to the superconducting properties. The analysis of different microstructural features in this study stresses the importance of considering macroscopic current paths when making a conclusion about the effectiveness of different dopants.

Experimental details
Commercially available MgB 2 powder (purity: 99%, Alfa Aesar) was used to prepare ex-situ MgB 2 bulk samples using an Ar glovebox to reduce air exposure. The details of the milling process have been given elsewhere [26]. Powders (∼3 g) after milling for 6 h were pressed into disc-shaped pellets for consolidation. Based on our preliminary work [25], 5 wt.% Mg addition was used in this study. Mg powder (purity: 99.8%, Alfa Aesar) was homogenously mixed by hand with ball-milled MgB 2 powder.
For studying co-additions in MgB 2 bulk samples, MgB 2 powder, Mg powder and hBN nanoparticles (average particle size <150 nm, Sigma-Aldrich) were used. The 1 wt.% hBN was mixed with MgB 2 powder manually in the glove box under an Ar atmosphere. After 6 h of milling, hBN + MgB 2 powder was transferred to a glass jar. Next, 5 wt.% Mg was added to the mixture and thoroughly mixed by hand for 5 min before being uniaxially pressed into pellets. A Dr Fritsch DSP 507 FAST apparatus was used to process bulk samples under vacuum. The uniaxial pressure was ramped up as the temperature increased and held at 50 MPa once the temperature reached the preset value. The sintering process was carried out from temperatures ranging from 900 • C to 1200 • C. Table 1 summarises the processing parameters of each sample.
X-ray diffraction (XRD) was performed using a PANalytical Empyrean diffractometer with Cu-K α radiation (0.154 nm) at 40 kV and 40 mA. Rietveld refinement was executed by using PANalytical HighScore Plus software to obtain phase fraction, lattice parameters, crystallite size and micro strain. Microstructural characterisation and chemical composition analysis were performed using a Zeiss Merlin field-emission scanning electron microscope (FEG-SEM) equipped with an Oxford Instrument 150 mm 2 Xmas energydispersive x-ray (EDX) detector. The grain size and crystallographic texture were examined by a Zeiss Merlin FEG-SEM with Bruker electron backscatter diffraction (EBSD) camera operating at 20 kV and 10 nA. The corrections of pattern background and the pattern indexing were performed by Bruker ESPRIT software, and the data post-processing were carried out by HKL Channel 5 software. Magnetisation measurements were carried out by a 16 T Quantum Design Physical properties measurement system with a vibrating sample magnetometer. The critical temperature measurement was performed at 5 mT, and moment-field sweeps were taken at 20 K. Bean's critical state model was used to calculate J c values as a function of applied field [27]. Figure 1 shows XRD patterns of MgB 2 bulk samples doped with both 1 wt.% hBN and 5 wt.% Mg and consolidated at different temperatures. Figure 1(b) highlights the evolution of impurity peaks. The complicated crystal structures of these B-rich compounds often make it difficult to distinguish the   peaks from different impurity compounds. For instance, the three strongest peaks of the MgB 4 and MgNB 9 phases are listed in table 2, and show significant overlap. In this case, critical factors to tell these two phases apart are: (i) the appearance of the strongest peak of MgB 4 at 35.4 • , (ii) the intensity of peaks at 38.8 • and 40.6 • which would indicate the dominance of MgNB 9 and (iii) the higher peak intensity at around 32 • in the MgNB 9 pattern compared with that produced by MgB 4 . Using this analysis, the MgB 4 impurity phase is prominent in samples sintered at 1000 • C and 1100 • C, but increasing the temperature to 1200 • C leads to the formation of more MgNB 9 . The quantitative results from Rietveld refinement are presented in table 3. No significant difference can be detected in the phase distribution between the 1hBN-5Mg-1000C and 1hBN-5Mg-1100C samples, but the fraction of MgB 2 decreased in the sample processed at 1200 • C, along with the detection of MgNB 9 (8 wt.%) and Mg (2 wt.%). A reaction between hBN and MgB 2 to form MgNB 9 has previously been reported in MgB 2 bulk samples: MgB 2 + BN ⇌ MgNB 9 + 3Mg [26], and the Mg peaks in XRD patterns from the 1hBN-5Mg-1200C sample provide supporting evidence that this reaction occurs in our samples.  The microstructure of MgB 2 samples with both Mg and hBN additions is strongly influenced by the processing temperature. As shown by the SEM images (figure 2(a)), the codoped sample processed at 1000 • C has a high porosity, with MgB 2 agglomerates (∼10 µm in size) distributed in a matrix of much finer particles. Although a number of small pores still exist in 1hBN-5Mg-1100C, the sample density has greatly improved. As the temperature goes up to 1200 • C (figure 2(c)), the sample inhomogeneity increases significantly, with dense MgB 2 regions up to hundreds of microns in size separated by regions that are apparently less dense.

MgB 2 samples co-doped with Mg and hBN
To identify the impurity phases in these samples, EDX analysis was conducted (figure 3). In the 1hBN-5Mg-1100C sample, areas rich in boron are not accompanied by the accumulation of nitrogen, as shown by the yellow dotted lines in figure 3(a), which is in agreement with the XRD results that indicate the main impurity phase is MgB 4 in this sample. It can also be seen that the MgB 4 particles, with sizes ranging from nanometres to around 10 µm, are situated within the porous matrix but not in the dense regions. The line scan results reveal the presence of ultra-fine N-containing impurities at some grain boundaries in the dense MgB 2 regions ( figure 3(b)). The arrows highlight that the increase in N-signal corresponds to a decrease in the fraction of boron compared to the MgB 2 matrix, indicating these impurities may be unreacted BN. In contrast, in the sample processed at 1200 • C, the B-rich particles are also rich in N, and are distributed in clusters outside large, dense MgB 2 regions (figure 3(c)). The line scan in figure 3(d) across features of the kind with the darker contrast in figure 2(c) shows an increase in B content and decrease in Mg content co-located with the N, indicating the transformation of MgB 4 to an Mg(B,N) phase. Additionally, the area fraction of the N-containing impurity phase is much larger than in the lower temperature 1hBN-5Mg-1100C sample. Although the quantification of light elements by EDX is imprecise, the measured composition for this phase is consistent with the presence of MgNB 9 peaks in the XRD pattern (figure 1). Figure 4 compares microstructures of dense MgB 2 regions and the more porous matrix in the bulk samples at higher magnification. In contrast to the typical dense region shown in figures 4(a) and (b) shows the lack of neck formation and growth between powder particles in the porous matrix, indicating that mass transport is inadequate at 1000 • C to achieve significant densification. In figure 4(c), polycrystalline MgB 2 grains in the dense regions of the sample processed at 1100 • C are well-connected, although some small MgO particles are located at the grain boundaries. However, in the porous matrix, numerous small MgO impurities around the MgB 2 particles are expected to impair electrical connectivity and impede densification. Increasing the processing temperature to 1200 • C results in a significant increase in both the amount and size of MgO particles, as a result of faster diffusion. However, a counter-intuitive decrease in MgB 2 grain size is observed (figure 4(e)) at high temperatures. Although higher processing temperatures would be expected to lead to larger grain sizes, we suggest that the accelerated formation of both MgO and MgNB 9 second-phase particles at 1200 • C (figures 4(c) and 5) can restrict the grain growth by strong Zener pinning model [28,29]. The darkest atomic number contrast of the MgNB 9 clusters is shown in the backscattered electron (BSE) image (figure 4(g)).
The use of EBSD to analyse phase distributions in these samples is limited by the difficulty in reliably distinguishing between nanoparticles of MgB 4 and MgNB 9 . However, since the aim of this characterization work is to understand the development of superconducting paths through the microstructure, we have decided to use the more reliable EBSD data from MgB 2 grains to concentrate on analysing the connectivity of the superconducting phase. Even though isolated small impurity phases can act as effective pinning centres, if pores and insulating impurities of any kind are clustered between superconducting grains they will act as severe obstacles to macroscopic supercurrent flow. The phase maps in figure 5, where the black 'unsolved' regions capture the distribution of insulating regions like nano-sized impurities (MgO, MgNB 9 and MgB 4 ) and pores like those in the images in figures 4(c) and (e), show clearly the overall connectivity of the MgB 2 . As the processing temperature increases from 1100 • C to 1200 • C, the areal fraction of zero-solutions increases from 13% to 19%, but in both cases the overall connectivity of the sample is compromised by non-superconducting phases (including porosity) located between the MgB 2 grains. The grain size distribution of both samples is shown in figure 5(c), and a slightly higher fraction of grains below 200 nm can be observed in 1hBN-5Mg-1200C than in 1hBN-5Mg-1100C.

MgB 2 bulk samples doped with Mg
XRD patterns of bulk samples with only 5 wt.% Mg addition are presented in figure 6. No peaks corresponding to residual Mg could be detected in any sample. In addition, there is little effect of changing the temperature from 1000 • C to 1200 • C in terms of the measured phase fractions of impurity phases, as demonstrated by Rietveld refinement giving MgB 4 and MgO fractions around 3 wt. % and 11 wt.%, respectively. Figure 6(b) shows that the intensity of the MgB 2 (002) peak increases with the processing temperature, indicating better MgB 2 crystallinity.
The BSE images in figures 7(a) and (b) show the contrast variations between the light grey, dense MgB 2 regions The matrix in 5Mg-1000C is highly porous, whereas fewer pores remain in the 5Mg-1200C sample showing significant densification has occurred at the higher temperature. MgB 2 grain boundaries are decorated with MgO impurities, as shown in the inset to figure 7(d).

Phase analysis and microstructural evolution
Quantitative results from Rietveld refinement of the XRD data from all the bulk MgB 2 samples sintered at 1200 • C are summarised in table 4. Included for comparison are data from our previously reported samples prepared from unmilled MgB 2 powder [30] and 6 h ball-milled undoped and 1 wt.% hBN doped (1hBN-1200C) MgB 2 [29], all processed at 1200 • C by FAST.
It can be seen that ball milling greatly decreases the crystallite size (from 170 nm to 62 nm), demonstrating the efficiency of ball milling on grain refinement. Our previous study shows that the MgO content in as-received MgB 2 powder is around 4 wt.% compared with 5 wt.% in 6 h-milled MgB 2 powder [26]. This indicates that a small fraction of MgB 2 powder may be oxidised during ball milling. However, the difference in the MgO content of bulk samples prepared from unmilled and 6 h-milled powder is much higher after sintering (8 wt.%  vs. 19 wt.%), as shown in table 4. We suggest that this can be explained by ball milling breaking up MgB 2 agglomerates and creating freshly exposed surfaces of MgB 2 grains, which can absorb more free oxygen or moisture during subsequent handling than unmilled powder. The process of MgB 2 oxidation during sintering is complex because it relates to both the availability of oxygen and the likelihood of MgB 2 decomposition which depends on the partial pressure of Mg vapour. Processing in vacuum reduces the formation of MgO [31,32] in comparison to the significant amount of MgO formation resulting from processing in air [33]. The MgB 2 decomposition rate also increases with processing temperature, and MgB 2 is thermodynamically stable only under high overpressures of Mg vapour [32,34]. Therefore, without Mg addition, the oxygen trapped during ball milling may enhance the decomposition of MgB 2 (19 wt.% in MgB 2 vs. 11 wt.% in 5Mg-1200C) because MgO has a much more negative Gibbs free energy of formation than MgB 2 [35].
The separate additions of 1 wt.% hBN or 5 wt.% Mg reduces the amount of MgB 4 by 31% and 81%, respectively, compared to MgB 2 without dopants. The former effect arises primarily from the production of MgNB 9 [26], while the latter results from the reaction of pre-existing MgB 4 with the added Mg to form new MgB 2 . In the co-doped MgB 2 samples, both  0.14 a The MgB 2 sample prepared from un-milled powder and processed at 1200 • C. b Samples that have been discussed in another study [26]. In the undoped MgB 2 sample, there is a thick layer of finer grained material surrounding the well-connected MgB 2 dense regions, in which smaller MgB 2 and MgB 4 grains are decorated by fine MgO impurities. The addition of Mg results in a significant decrease in the MgO content that will help to improve intergranular connectivity to some degree, as shown in the 5Mg-1200C sample ( figure 7(d)).
The different types of microstructures produced under different processing conditions and additions are summarised schematically in figure 9. Bulk samples produced from the as-received MgB 2 powders contain large MgB 2 agglomerates and MgB 4 impurities. Ball milling can refine particles but also leads to the characteristic bimodal distribution of powder particle size (i.e. large polycrystalline aggregates and poorlyconnected finer grains) [26]. However, adsorption of adventitious oxygen on the new surfaces of aggregate particles and loose MgB 2 grains that form during ball milling has the result of hindering not only the macroscopic connectivity between the dense regions and the matrix but also intergrain connectivity in the matrix in consolidated bulk samples (M1, figure 8). In comparison, the addition of Mg prevents MgB 2 decomposition and partially alleviates the oxidation problem, as evidenced by the observation of fewer MgO particles at MgB 2 grain boundaries and the boundaries between dense regions and the matrix in figure 7(d) compared with figure 8 (M2, figure 7(d)).
When hBN nanoparticles were ball-milled with MgB 2 powder, they may distribute among MgB 2 aggregates and grains. Mg addition provides a liquid sintering environment during the sintering process, and high temperatures (1200 • C) will lead to the dominance of MgNB 9 impurity clusters, separating the MgB 2 grains in the matrix into small clusters ( figure 4(f)). Moreover, the grain connectivity in dense regions  is impaired as well (M3). Other fine impurity phases such as MgB 4 and hBN may also exist in these samples though they are difficult to detect by XRD and EBSD measurements, so we have included them in the schematic for the M3 system. Lowering temperatures to 1100 • C can avoid the severe reaction with hBN to form MgNB 9 , so MgB 4 is still the primary impurity phase. However, the distribution of hBN nanoparticles and MgO impedes the sintering of MgB 2 grains, and results in higher porosity in the matrix (M4, figure 4(d)).
At 1000 • C, MgB 2 grains in the matrix are almost unsintered, and thus there is almost no connection between different dense MgB 2 regions via the matrix (M5).  around 38 K, but samples singly doped with either hBN or Mg have slightly sharper superconducting transitions than the undoped and co-doped ones when processed at 1200 • C. ∆T c is broadened to around 2 K in Mg-MgB 2 samples prepared at the lower temperature of 1000 • C, figure 10(b). A similar trend can be found in hBN and Mg co-doped MgB 2 sample series in figure 10(c), where a much wider ∆T c (∼6 K) is observed in 1hBN-5Mg-1000C. Broad ∆T c indicates the large variance in local T c values in the samples, which may arise from material inhomogeneity. The matrix in the samples processed at 1000 • C is highly porous, with no evidence of the formation of sintering necks between MgB 2 grains, in contrast to the well-connected MgB 2 regions. We speculate that, in this case, the lattice strains introduced by the ball milling process are difficult to recover due to limited diffusion at lower temperatures. As a result, these grains may have a lower T c than grains within the dense regions. Mg addition may partially alleviate the inhomogeneity due to the acceleration of mass transport.

Superconducting properties
J c (B) curves calculated from magnetization loops taken at 20 K using Bean's critical state model are shown in figures 10(d)-(f). Similar data for pure MgB 2 and 1hBN-MgB 2 are also plotted in figure 10(d) to aid comparison of the effect of different types of dopants on samples processed at 1200 • C [26]. It is clear that adding either 5 wt.% Mg or 1 wt.% hBN leads to a significant improvement in J c (B) curves at all magnetic fields compared with the undoped MgB 2 , with 5Mg-MgB 2 out-performing 1hBN-MgB 2 at fields above 1 T. However, the combination of 1 wt.% hBN and 5 wt.% Mg failed to give a synergistic effect on J c values in the co-doped MgB 2 sample. Instead, the co-doped sample showed poorer performance than both of the singly-doped samples over the entire field range, with even the undoped MgB 2 having better J c values at high magnetic fields. Figure 10(e) compares J c curves of 5Mg-MgB 2 samples processed at different temperatures. Matthews et al added Mg to commercial MgB 2 powder and prepared ex-situ MgB 2 bulk samples at 900 • C by FAST. They found that liquid phases can form during the sintering which helps improve the bulk density. Therefore, the low-field J c was enhanced by Mg additions, in particular 6 wt.% and 10 wt.% Mg [25]. However, large pores up to hundreds of microns still remain in their best sample. In comparison, in this study we introduced ball milling and increased the processing temperatures and found J c in both the 5Mg-1100C and 5Mg-1200C samples is enhanced over the entire field range, which we ascribe to the elimination of large gaps between dense MgB 2 regions which enables the current to flow on a larger length scale, corresponding to the change in microstructural model from M5 to M2 (figure 9). The improved J c performance results from the application of ball milling, which refines the powder particles without introducing so much MgO as to reduce interconnections. The Mgdoped samples in this study have comparable J c curves at high magnetic fields regardless of the processing temperature, but the self-field performance of the samples processed at 1100 • C and 1200 • C are around 1.8 times higher than the sample processed at lower temperature (5Mg-1000C). This poor self-field performance is also seen in the co-doped sample processed at low temperature (figure 10(f)), and results from the poor intergranular connectivity in these samples (M5 vs. M4 in figure 9). Interestingly, in contrast to the Mgdoped samples, the co-doped sample processed at 1100 • C considerably outperforms the equivalent sample processed at 1200 • C in the high field range.
To understand these observations, it is important to acknowledge the limitations of using Bean's model to extract J c -B from magnetization measurements for inhomogeneous samples [26,30]. Complexity arises because local currents circulating within well-connected microscopic domains contribute to the measured magnetic moment. Bean's model assumes that the measured magnetic moment arises solely from macroscopic current loops circulating homogeneously throughout the whole bulk. This approximation is valid provided the sample is relatively well connected, as the contribution to the total magnetic moment from microscopic current loops within isolated regions will be much smaller than the contribution from the macroscopic current loops. However, if the sample is poorly connected, the macroscopic J c will be low and the magnitude of the microscopic current loops may no longer be negligible. If this is the case, the J c values extracted with Bean's model using the sample dimensions will relate neither to the macroscopic J c nor the intrinsic J c within the well-connected regions.
In the majority of the samples reported here, the connectivity is good enough that the J c values extracted using Bean's model can safely be interpreted as the macroscopic J c . A possible exception is the 1000 • C processed co-doped sample, which has much poorer low-field performance than the other samples and shows an upturn in J c at low field indicative of a very low self-field [36]. This suggests that microscopic current loops may be making a significant contribution to the measured magnetic moment, and the extracted J c values are not easy to interpret. The poor macroscopic connectivity in this sample is evident in the SEM images (figure 2(a)) that clearly show the lack of sintering.
Another complication with interpreting the J c -B performance arises as a result of the intrinsic anisotropy of MgB 2 that leads to B ||c c2 < B ||a,b c2 . As discussed by Eisterer et al [37], the grain orientation relative to the direction of the applied magnetic field affects the maximum current that an MgB 2 grain can carry. This means that, as the magnetic field is increased, superconductivity in unfavourably aligned grains switches off and the supercurrent has to divert around them. The consequence is that J c drops off more rapidly than predicted by the Dew-Hughes or Kramer models [38,39] when the magnetic field increases above B ||c c2 , reaching zero when there is no longer a percolation path through the remaining superconducting grains. Therefore, the shape of the J c -B curve is not only determined by B ||c c2 and B ||ab c2 values and the flux pinning mechanism, but also by microstructural features that influence supercurrent percolation. For example, the presence of nonsuperconducting impurity grains reduces the co-ordination number of MgB 2 grains in contact with other MgB 2 grains, effectively increasing the percolation threshold and leading to a more rapid decrease in J c with magnetic field [34]. This percolation effect may explain the poor high-field performance of the 1200 • C co-doped sample, which has a significant fraction of MgNB 9 impurity grains finely distributed throughout the MgB 2 matrix (figure 4(f)) and the distribution of insulating regions (figure 5), shown as M3 in figure 9. The co-doped sample processed at 1100 • C shows superior highfield properties because the reaction to form the MgNB 9 phase occurs more slowly at lower processing temperatures, so there are fewer impurity grains impeding current percolation (M4 in figure 9).

Conclusions
Ex-situ MgB 2 bulk samples with Mg addition and Mg/hBN coaddition have been prepared using FAST. Our previous work has shown that hBN doping can improve the J c performance of MgB 2 bulk samples by improving flux pinning, whereas Mg additions improve the connectivity of samples through liquid phase sintering. One aim of this work was to attempt to exploit both of these effects using co-doping. Unfortunately, the properties of the co-doped samples did not match those of the single-doped Mg or hBN samples owing to the presence of Mg liquid during sintering accelerating the formation of MgNB 9 . This impurity phase, distributed as fine grains within the MgB 2 matrix, was found to be detrimental to the superconducting performance, particularly at high fields. Additionally, we used ball milling to prepare Mg-MgB 2 samples and increased processing temperatures from 900 • C to 1100 • C to eliminate the large gaps between regions of dense MgB 2 previously identified. A considerable improvement in J c -B performance has been achieved.
Another goal of this study is to develop different models of the observed microstructures, and to correlate these models to the superconducting performance, stressing the importance of the length scale over which transport currents can flow. We have shown that the effectiveness of different impurity phases can be understood if their effect on the microstructure formed during processing is carefully analysed. Moreover, the summary of microstructural models lays a foundation for a more fundamental approach to establish a theoretical basis to explain J c curves in MgB 2 more effectively than a simple use of Bean's model.

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).