Distribution of the superconducting critical current density within a Gd–Ba–Cu–O single grain

The magnitude of the maximum trapped magnetic field in a bulk, single-grain superconductor is a key performance figure of merit. This is determined, generally, by the magnitude of the critical current density, Jc, and the length scale over which it flows. As with all type-II superconductors, Jc is related closely to the microstructure of the superconducting material and, in the case of RE–Ba–Cu–O [(RE)BCO, where RE is a rare-earth element or yttrium] single grains, RE2BaCuO5 (RE-211) inclusions in the superconducting REBa2Cu3O7−δ (RE-123) phase matrix are key microstructural features that act effectively as flux pinning centres. Although the distribution of RE-211 in single-grain bulk superconductors has been studied extensively, the variation of Jc within a given sample has been much investigated much less thoroughly. A detailed experimental understanding of the variation of Jc in these technologically important materials, therefore, is required given the growing popularity and significance of numerical techniques for modelling the behaviour of type-II bulk superconductors. Here we report a systematic investigation of the correlation between Gd-211 particle density and sample porosity, which are microstructural features, and Tc and Jc in a Gd–Ba–Cu–O bulk, single grain fabricated using a buffer layer and a supply of additional liquid phase. This was performed by cutting the sample into numerous sub-specimens of approximate dimensions 1.8 × 2.8 × 1.5 mm3. We observe that Jc decreases with distance from the seed, although more strongly with distance along the c-axis than along the a–b plane. In contrast to what might be expected given the assumed contribution of RE-211 inclusions to flux pinning, we find no evidence of a clear correlation between the local RE-211 precipitate density and local critical current on a length scale of mm. We observe that the porosity of the sample is a more dominant factor in determining the distribution of Jc within a single grain.


Introduction
The presence of grain boundaries in RE-Ba-Cu-O [(RE)BCO, where RE is a rare-earth element or yttrium] bulk superconductors, misoriented by more than a few degrees, limits significantly the macroscopic superconducting properties of these potentially technologically important materials [1,2]. As a Superconductor Science and Technology Supercond. Sci. Technol. 33 (2020) 044009 (12pp) https://doi.org/10.1088/1361-6668/ab6dc2 1 Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. result, bulk (RE)BCO superconductors suitable for practical applications have to be fabricated in the form of large, single grains with uniform superconducting properties throughout the sample microstructure. Unfortunately, however, the critical current density, J c , in these materials is observed to vary significantly both within a single grain and between single grains notionally fabricated by the same melt processing technique. This variation is intrinsic to the melt growth process employed and to the ceramic-like nature of these materials, which typically contain microcracks within the sample microstructure. The ability of bulk superconductors to generate trapped magnetic field depends directly on the critical current density, although mechanical weakness in the sample microstructure may result in their premature failure under the action of Lorentz forces in the presence of large applied magnetic fields. Critical current density, however, depends on a wide variety of factors ranging from the effectiveness and density of pinning centres on the length scale of the vortex core to material defects and grain boundaries, porosity and cracks at the mesoscopic scale.
Bulk superconductors consist typically of a single grain, fabricated usually by a melt process, which is composed of a continuous superconducting (RE)Ba 2 Cu 3 O 7−δ phase matrix (RE-123-where RE=Nd, Sm, Gd, Dy, and Y or combined RE element) with embedded, discrete RE 2 BaCuO 5 precipitates (RE-211) that act as effective flux pinning sites. Most studies of these materials report typically only a single J c -B curve obtained from one specimen at one position within a given sample, which contains relatively little useful information about the applied potential of the complete single grain. In addition, reported J c (B= 0) values in Y-Ba-Cu-O single grains can vary from 2×10 4 to 2×10 5 A cm −2 at 77 K [3][4][5][6][7]. Dewhurst et al reported the distribution of J c across the entire cross-section of a YBCO single grain [6]. One of the conclusions of this investigation was that J c of the sample in the region directly below and adjacent to the Sm seed crystal exhibited a lower J c by almost a factor of 3 relative to the surrounding material [6]. These authors postulated that this was due to Sm contamination from the seed crystal, which had the effect of locally reducing T c [8]. This suggests that the distribution of the local J c in bulk superconductors is not only affected critically by the sample microstructure, but also by any local variation in T c . The development of the so-called buffer seeding technique [9][10][11][12][13][14] has helped to improve the reliability of the seeding process, and has ameliorated the problem of contamination from the seed reported in these early studies.
This paper reports the results of experiments aimed at obtaining a systematic understanding the distribution of local J c in bulk (RE)BCO superconductors. This involves examination of the entire cross-section of a GdBCO single grain fabricated in air by the so-called top seeded melt-growth (TSMG) technique [15] using the buffer seed technique. The single grain sample was divided into many sub-specimens and the T c and M-H characteristic of each sub-specimen measured at 77 K. The microstructure of each sub-specimen, including porosity and the size and distribution of Gd-211 particles, was analysed at positions within the parent single grain and correlated with the J c measurements. The observed trends and range of fluctuations in local J c of the GdBCO single grain are discussed in detail.

Melt-processing
The raw powders of Gd-123 and Gd-211 were sourced from Toshima, 99.9% purity (grain size: Gd-123, 2-3 μm; Gd-211, 1-2 μm). The base Gd-Ba-Cu-O standard powders were of composition [75 wt% GdBa 2 Cu 3 O 7−δ (Gd-123)+25 wt% Gd 2 BaCuO 5 (Gd-211)]+0.5 wt% CeO 2 . The precursor powders were mixed thoroughly using an automatic pestle and mortar for 2 h and prior to pressing into a pellet of mass 20 g for melt processing using the arrangement shown schematically in figure 1. A generic seed [16] (of composition [(Nd123+0.12 Nd422)+1 wt%MgO]) was placed at the centre of the top surface of the assembly and a buffer [12,17] was inserted between the seed and the pellet. The composition of the buffer was 75 wt% Gd-123+25 wt% Gd-211 for the GdBCO sample. A liquid-rich phase substrate was used to prevent unwanted grain nucleation at the bottom of the sample, in addition to supplying liquid Ba 3 Cu 5 O 8 back to the pellet during melt growth [18,19].
The entire arrangement of the pellet, buffer, generic seed and substrate was placed in a box furnace, heated to 1080°C at 70°C h −1 and held for one hour. The arrangement was then cooled at 50°C/h to 1035°C, then more slowly at a rate of 0.8°C h −1 to 1025°C then at 0.4°C h −1 to 1000°C. Finally, the sample was furnace-cooled to a room temperature. The sample was annealed ultimately in a tube furnace in an oxygen atmosphere at 450°C for 7 d to allow oxygen to penetrate into the single grains and to transform the Gd-123 lattice structure from tetragonal to orthorhombic, which is the target superconducting phase [20].

Measurements and microscopy
The single grain sample was polished flat and its trapped field measured at 77 K. This involved cooling the sample to 77 K in a magnetic field of 1.4 T and removing the applied field over a period of 100 s. A hand-held Hall probe was placed 0.5 mm above the top surface of the sample to determine the maximum trapped magnetic field, with the complete trapped field profile measured subsequently using a rotating array of eighteen Hall probes placed 1.5 mm above the sample surface. The sample was cut along a diameter and through its entire thickness following measurement of the trapped field, as indicated by the two dashed red lines in figure 2(a).
A thin slab was extracted from the single grain sample and then cut further parallel to the c-axis and cleaved along the ab plane into smaller sub-specimens corresponding to locations 1ta, 1tc, etc, each of approximate dimensions a×b×c at 1.8×2.8×1.5 mm 3 , as shown schematically in figure 2(b). The red dashed line in figure 2(b) indicates the approximate position of the boundary between the A-and the C-growth sectors. T c and M-H loops of the sub-specimens (24 in total from locations 1ta to 4ta of the first row to 1tf to 4tf of the sixth row) were measured using a superconducting quantum interference device (SQUID). This involved applying a test field of 2×10 −3 T perpendicular to the ab plane of each sub-specimen for the measurement of T c and using the extended Bean model [21] to calculate J c using M-H loop data measured for each cuboid, a×b×c, at 77 K, where a, b, and c are the dimensions of the sample with a<b and c is the specimen dimension in the c direction.
The cross-section of the remaining half sample was polished, and its microstructure examined using an OLYM-PUS BX51M optical microscope. In total, 85 images at a magnification of 50× were assembled automatically by LAS BX51M software to reveal the distribution of the pores and cracks over the cross-sectional surface of the sample. Images at higher magnification (500×) were also taken from the edge of the sample to its centre and from the top to the bottom of the half-grain at intervals of 1 mm to examine the distribution of Gd-211 inclusions in order to investigate correlations between local J c and the associated single grain microstructure. The total count, fraction of area occupied by pores and the average size of the pores of 20 images cropped from figure 4(b) at position exactly equivalent to the positions where J c were measured were estimated quantitatively using ImageJ software. 20 additional photographs of the crosssection of the sample were taken by SEM at a magnification of 5000× along the a-and c-axes, starting from the central position and 0.5 mm below the top surface. The area fraction occupied by the Gd-211 inclusions and their average size along the a-axis were measured quantitatively using ImageJ software. The single grain was assumed to exhibit a radial symmetry throughout this study.

Results and discussion
Confirmation of single grain growth   over the entire sample volume, so its contour map should consist of concentric, closed lines that follow roughly the shape of the single grain. Figures 3(b) and (c) show the contour map and B z -X-Y measured by the rotating Hall probe array at a position 1.5 mm above the top surface of the sample. It can been seen further that the sample does, indeed, constitute a single grain from the geometry of the trapped field profile. The peak value measured by the hand probe 0.5 mm above the top surface of the sample is 0.65 T, which is close to the typical value of a GdBCO single grain of this geometry observed previously by our group [22], suggesting that the sample is suitable for analysing the distribution of the local superconducting properties within the body of the single grain.

Microstructure
Low magnification at 50×. Figure 4(a) shows a photograph of the cross-section of the GdBCO single grain. Figure 4(b) shows an assembly of 85 photographs taken using an optical microscope at 50× magnification over the entire cross-section of the sample. Both images are typical of (RE)BCO single grains (where RE=Nd, Sm, Gd, Dy and Y) fabricated in air. Figure 4(b) shows an image of higher resolution than that in figure 4(a), that gives more detail of the microstructure evident on the polished surface, which can be divided into three regions (1-3). There are many pores within region 1 (the red dashed rectangle); the size of the pores is roughly 50 μm on average and it can be seen that the closer to the sample centre, the larger the pore size. A large crack, which was almost certainly caused during the precursor compaction process, crosses the centre of the sample cross-section. Region 2 (between the red dashed line and yellow dashed line), of thickness of 2-3 mm, exhibits significantly reduced porosity and the material appears relatively dense in this region. There are many small, parallel cracks, which are caused during oxygenation as the tetragonal Gd-123 phase transforms to the orthorhombic phase [23]. Region 3 (outside the yellow dashed line) consists of the edges of the sample and where the growth process terminates. It can be seen from the contrast in figure 4(b) that the material in region 3 appears to be different to that of the rest of the sample. The relative proportion of the size of regions 1 and 2 changes from sample to sample, depending on the particular (RE)BCO system, the composition of the precursor powder and the processing route. Published photographs of the cross-sections of YBCO single grains [17,19,24,25] indicate further that all single grains within this system can also be divided, generally, into these three regions. Region 3 is characteristically quite small, of size between 0.5 and 1 mm at the circumference edge and 2 mm at the bottom of the sample in this study, although its thickness may change depending on the substrate material used for the growth of the single grain. Figure 5(a) shows the total count of pores at 4 positions in all the sample layers (a to e). It can be seen that the total pore count at positions 4 (purple triangles) and within the 'a' layer, which are within the 2nd region in figure 4(b), is low. In addition, there is a sharp increase in porosity in position 2 in all b, c, and d layers and the porosity remains approximately constant right up to the edge of the sample. Figure 5(b) shows the average size (derived from the longest dimension present in a pore) of pores at 4 positions in the different layers. It can be seen that the size of the pores are smaller in the 'a' layer and the pore size increases with increasing proximity to the centre of the sample. The average longest dimension of the pores is 100 μm measured by ImageJ software. Figure 5(c) indicates that the area occupied by the pores can be as high as 25% in the b, c and d layers, which suggests that up to 25% of the cross-section of the single grain sample may not be superconducting.
Gd-211 distribution. Figure 6 shows the microstructure of the GdBCO sample at position 28 (see figure 2(b)). The sample exhibits a typical microstructure expected for a (RE)BCO single grain on this length scale. The continuous background is the superconducting Gd-123 matrix, and the light-incontrast inclusions are the embedded, non-superconducting Gd-211 particles. The size of the Gd-211 inclusions varies from 1 to 6 μm, with most particles being approximately 2 μm in diameter. There are local areas within the sample microstructure, such as that circled, that are void of Gd-211 particles. It is suggested that these areas were initially pores that became filled by the liquid phase (Ba 3 Cu 5 O 8 ) at elevated temperature, which later reacted with Gd-211 to form the Gd-123 phase during the growth process [26,27]. A single pore can be seen at the bottom of figure 5, which is expected for an image magnification of 500×, and particularly in photographs taken in the vicinity of the centre of the sample cross-section. Figure 7 shows a number of photographs taken at a magnification of 500× at different positions within the single grain sample, and from which the distribution of Gd-211 second phase inclusions can be studied. It can be seen that the number of Gd-211 particles in each image in the a/b growth direction increases and their size becomes slightly smaller with increasing distance (photographs 011, 007 and 002; top row, right to left). This trend can be seen more clearly from the photographs taken at a magnification of 5000× in figure 8. Comparing figures 8(a) and (b), it can be seen that the Gd-211 particles increase in quantity but decrease in average size at a position of 5 mm along a-axis. This trend is also indicated by the quantitative analysis of the area fraction occupied by Gd-211 particles and their average size from the SEM images at a magnification of 5000× along the a-axis, shown in figure 8(d). Photographs 011, 032, 053 and 075 (right-hand column of figure 7, top to bottom) show the Gd-211 distribution along the c growth direction, which follows a similar trend, which also can be seen more clearly from the SEM images taken at a magnification of 5000×, shown in figure 8. Comparing figures 8(a) and (c), it can be seen that the Gd-211 particles increase in quantity but decrease in size with increasing distance along the c-axis. The number and size of the Gd-211 inclusions is similar along a given growth front, on the other hand, as indicated by the parallel dashed green lines in figure 2 (apparent by comparing photographs 53 and 49). Many researchers have reported this trend, in the YBCO [28,29], GdBCO, SmBCO and Ag-containing (RE) BCO systems [24,[30][31][32][33], and the current study confirms this trend that the amount of embedded Y-211 inclusions along both the a/b and c crystallographic growth directions increase under processing conditions of a larger under-cooling temperature, which leads to the formation of a region of low Y-211 concentration in the vicinity of the seed [33].
This distribution of RE-211 content within a single grain is an intrinsic characteristic of the top-seeded melt growth (TSMG) process and can be explained by the so-called push/ trap effect [30]. According to pushing/trapping theory, Y-211 particles of size smaller than a critical radius r * will be pushed by the growth front of the Y-123 single grain. In other words, Y-211 particles of size larger than r * will be trapped within the growing Y-123 single grain matrix. r * is also inversely proportional to the growth rate, which is influenced critically by the undercooling and the initial Y-211 composition. In general, the higher undercooling, the lower r * , which is the case at positions further away from the seed. Although RE-211 particles react with the liquid phase and are therefore not technically inert during the single grain growth process, the push/trap model still provides a very good approximation to the dynamics of the RE-211 particle during the grain growth process.
Comparison of the distribution of Gd-211 within the GdBCO single grain studied here with those reported previously indicates that a different trend is seen in the current sample, due primarily to the use of a buffer beneath the seed. The position under the buffer (1ta) has rather large quantity of RE-211 inclusions, as can be seen from figure 8(d), the blue dots at positions 0, 1 and 2 indicate that Gd-211 can occupy an area as high 20%. This compares to a steep spatial concentration gradient in RE-211 inclusions observed in the vicinity of the seed [33] when a buffer was not used, which can vary typically from 5% to 15% over a distance of 0-2 mm in all (RE)BCO systems investigated to date [24,33]. The use of a buffer and polishing the top surface of the single grain flat for the trapped field measurement resulted in the removal of approximately between 0.5 and 1 mm of material from the top surface of the as-grown sample. As a result, the number of Gd-211 inclusions under the position of the seed at specimen location 1ta is considerably greater than when a buffer is not used, as is apparent from photograph 011 in figure 6. This effect has also   been observed in the YBCO system [34] when a buffer was used in the TSMG process. That is to say, the distribution of Gd-211 is relatively uniform in this study, and especially in the vicinity of the seed (or buffer) in the polished top surface of the sample and in the region where microstructure affects significantly the measured trapped field. The region at the centre of the top surface of the sample, and where the RE-211 concentration changes rapidly, has been removed for the GdBCO sample studied here, even though the trend in the size and distribution of the Gd-211 phase is similar as that reported elsewhere.
The edges of the sample (i.e. at the ends of the grain growth process) are shown in figure 7 in the photographs in the left column and 0.5 mm beyond the point at which growth terminates in the 4th and 5th rows of the single grain. It can be seen that there is a large concentration of Gd-211 particles in the regions labelled as 002, 023, 044, 066, 071 and 075 in figure 7, which is anticipated from push/trap theory. Microstructures such as that shown in figure 9 at position 043, which was photographed a further 0.5 mm towards the edge of the sample, show a significant difference from that observed in the bulk of the single grain. The white-in-contrast substance in these micrographs is a Ba-rich phase solidified from the residual liquid phase and impurities, which has been analysed thoroughly in previous research. The microstructures at the very bottom of the sample are shown as 076, 080 and 086. Extremely large inclusions and regions of solidified liquid-rich phase are present in these areas.
In summary, the microstructures at magnifications of 50× and 500× of the polished GdBCO single grain of 20 mm in diameter fabricated by the buffer technique exhibits high  porosity at the centre of the sample and very low porosity at positions within 2 mm of the edge of the sample. The distribution of Gd-211 particles in the single grain microstructure is described well by push/trap theory, e.g. there are smaller and more Gd-211 at positions further away from the seed along the principal growth directions. However, this change is relatively small when compared to the distribution of RE-211 particles observed in single grains grown by melt processing without a buffer. The edges, either at the circumference or the bottom of the sample, contain a significantly higher concentration of Gd-211 and solidified liquid phase than the rest of the sample.
Superconducting properties: T c and J c at 77 K. Figures 10(a)  and (b) show the results of the measurements of T c for specimens located beneath the buffer along the c-axis and across the first-row along the ab plane, respectively. Figures 10(c) and (d) show the equivalent J c measurements at 77 K for these specimens. The onset values of T c of the specimens at locations 1ta, 1tb, 1tc and 1td in figure 10(a) are coincident at 93.5 K, and the measured values of ΔT c are all narrow, which indicates only limited Gd/Ba substitution in these samples and that there is little or no contamination from the seed due to the use of the buffer, as has been reported elsewhere [9,34].
However, the specimens at locations 1te and 1tf have a lower onset T c and generally exhibit a very broad transition. In particular, the magnetic moment of specimen 1tf (navy curve) is extremely low. This suggests that the volume fraction of superconducting material is reduced compared to that at other locations. Given that all the sub-specimens are of similar size, this can be explained by the location of specimen 1tf at the bottom of the sample, which increases the concentration of liquid-rich phase in its microstructure [25] and, as a result, reduces the volume of the superconducting phase. The onset T c 's at the edges of the single grain, such those observed at positions 4ta in figure 10(b) and 1te in figure 10(a), and at the circumference and bottom of the single grain, are also inferior to those of the other specimens. This is also due to the reduced presence of superconducting phase at these positions, and is associated microstructurally with either the end of the growth process or to the presence of an excess of Gd-211 phase inclusions, as evidenced from the microstructure images in figure 7. This effect from the edges also can be seen in the J c data in figures 10(c) and (d).
The J c -B curves in figures 10(c) and (d) were calculated using the extended Bean model. The 'tilt' in the GdBCO M-H loops is due to the paramagnetic nature of Gd, which is superimposed on the superconducting magnetic moment. As a result, the two values of the magnetic moment derived from the M-H loop to obtain ΔM (for increasing and decreasing field, respectively) are not symmetric about the x-axis (field is the x-axis), which leads J c (0) to be lower than J c (0.1) in some cases, such as the J c -B curve for specimens at locations 1tb and 3ta in figures 10(c) and (d). It was expected that specimen 1tf would exhibit low J c , given its broad T c and poor superconducting properties. The J c -B curves along the c direction in figure 10(c), however, show that sub-specimens 1ta and 1tb have consistently the highest J c at all applied fields and exhibits the 'peak' effect [35] (in which J c increases under the influence of an externally applied field, up to a threshold value), whereas other specimens, such as 1tc, 1td and 1te, exhibit similar J c -B curves at all applied fields and do not show the peak effect. Figure 11 shows the T c and J c -B curves of the remaining specimens in the single grain cross-section. The onset of T c is the same at 93.5 K, and ΔT c is relatively narrow except the edge of the parent sample in row f and column four. Similarly, J c decreases from top to bottom of the single grain for specimens 2ta to 2tf in figure 11(d), 3ta to 3tf in figure 11(e) and 4ta to 4te in figure 11(f). Significantly, the J c data shown in figure 11(f) are lower since these specimens are at the edge of the single grain. In general the J c -B curves are almost monotonic and hence do not intersect with each other. J c at 0.5 T is replotted with respect to location in figure 12.
It can be seen clearly from figure 12(b) that J c decreases along the c direction of the single grain. However, the trend along the a/b direction is not as apparent as that along c, with the measured values of J c in layers d and e being almost constant, except at the edges of the sample, where J c of specimens in column four are low. The values of J c in layers a, b and c along the a/b direction decrease from the centre to the edge of the sample relative to J c values observed at positions 4. J c at the specimen position immediately beneath the buffer is the highest, which is not the same as observed previously in an early investigation [6].
It is observed generally that J c is dependent on the volume fraction of RE-211 in the single grain microstructure  [36]. However, the previous research only suggests when the weight percentage of RE-211 is not changed, the resulted smaller and more numerous inclusions of RE-211 increase local J c , therefore trapped field [36][37][38][39]. The distribution of Gd-211 particles in this study, indeed, shows an increase in volume fraction with very little variation along both principal growth directions, although there is a small variation along the c direction. However, this is not sufficient to cause the observed trend in J c . It can be seen from figure 12(a) that values of the J c in layers a and b layers (black and red) are a factor of two larger than those in layers c, d and e. Although, theoretically, J c varies in proportion to the number of pinning centres, including stacking flaws, twins and Gd-211-related pinning sites, the distribution, and therefore contribution to trapped field, of these pinning centres within the bulk microstructure can be very complicated. The difference between layers a, b layers and layers c, d, e is that the latter appear to contain a greater number of large, non-superconducting defects and large pores that cannot work effectively as flux pinning centres towards the centre of layers b, c, d and e. By comparing the quantitative distribution of the porosity shown in figure 5 and the quantitative distribution of Gd-211 in figure 8(d) with figure 12(b), it is likely that the existence of these large non-superconducting pores contributes significantly to the lower observed values of J c in layers c, d, e. The negative contribution of this microstructural feature to J c is more pronounced than the positive contribution from enhanced flux pinning by the Gd-211 phase in this sample. This also explains why J c declines rather rapidly along the c-axis of the single grain due to the rapid change from a dense to a more porous material, and, finally, to a solidified non-superconducting phase from specimen positions 1ta to 1te. The highest value of J c (0.5) (specimen position 1ta) in the first row of the sample is 3 times the value of the lowest positioned specimen J c (0.5), even if the specimen at the edge (1tf) is discounted. The effect of microstructure (mainly porosity) on the value of local J c can also explain its observed trend along the a/b direction ( figure 12(a)). The variation in J c at the first, second and third positions in a particular layer is less (other than at specimen position 1ta) due to the similar observed levels of porosity up to the edge of the single grain (specimen position 4). The J c at specimen position 1ta is relatively high for other reasons, such as the integrity and alignment of the lattice to the orientation of the single crystal seed in the vicinity of the seed/buffer [13]. In summary, by comparing figures 5(b) and 12(b) in which the x-axes are the same, it can be seen clearly that the porosity is low and the values of J c high within the a layers, whereas for the remaining layers (b, c, d and e), the porosity is high and the values of J c low. It is not possible, therefore, for the distribution of Gd-211 particles to influence significantly the distribution of J c in layers b-e, given the non-superconducting nature of pores, which is a more dominant influence on J c .
It can be seen further that low J c occurs consistently in specimens in regions at the end of the growth process, which constitute the edges of the circumference of the single grain (specimens 4ta, 4tb, 4ta and 4td) and the bottom layer (f). This is consistent with the observed low T c for these specimens that also exhibit a very broad transition due to the presence of both a relatively large number of Gd-211 phase inclusions, solidified, non-superconducting liquid phase and impurities, which reduce J c much more severely than the presence of pores in an otherwise strongly superconducting phase matrix. In addition, the effect at the edges of the sample is more pronounced with increasing distance along the growth direction, as indicated by specimens 4te and 4tf, which exhibit the worst properties of T c and J c in the entire sample.
The observed trend in the distribution of J c is consistent with the results of a previous study [6] (figures 3 and 4 therein) allowing for contamination in the region beneath the seed, which reduces T c . J c in the middle layer of the single grain is also higher than that observed in the bottom layer [6]. However, the previous study of the distribution of J c did not measure the properties of specimens at the extreme edges of the sample, such as at locations 4, and the sample was not melt processed with a buffer. J c in the a/b direction in the present study is relatively constant, although it does fluctuate within a range of approximately±1500 A cm −2 in all layers (a, b, c, d and e) of the single grain (apart from J c at 1ta) if the J c values at positions 4 are not taken into account. The same trend in J c along the c growth direction has also been reported for the YBCO system [40] processed in air by TSMG using a buffer. It is clear, therefore, that J c decreases rather rapidly from top to bottom of the single grain along the c direction. On the other hand, J c is relatively constant within a given layer in the a/b direction and there is no clear correlation between the distribution of RE-211 and the local J c within one single grain.

Conclusions
Systematic examination of the cross-section of a GdBCO single grain fabricated by buffer-aid TSMG has shown that the sample can be considered to consist of three regions. The first region, at the centre of the grain, contains many pores, the second region, closer to the edges, is denser and the third region, at the very edges, is composed generally of a concentration of RE-211 particles and solidified liquid phase with embed impurities.
The number of Gd-211 inclusions increases gradually along both principal growth directions and their size becomes smaller, as reported previously for the GdBCO system. The presence of porosity in the single grain microstructure appears not to influence the distribution of the Gd-211 particles. However, the observed concentration gradient of the Gd-211 inclusions is less steep for the GdBCO sample investigated in this study, and especially in the region of the seed (around 1.5 mm in diameter). This is attributed to the use of a buffer and the polished surface of sample, which increases the effective concentration of Gd-211 particles at the centre of the top surface of the single grain.
J c decreases along the c-growth direction from top to bottom of the single grain, but varies much less along the a/b direction, ignoring the edges of the sample. The same distribution has been reported for YBCO single grains, for which RE/Ba substitution effects are not an issue (i.e. the onset T c is high and ΔT c is narrow for the entire sample away from the sample edges).
The effect that the edges of the sample exhibit the lowest and the broadest T c hence lowest J c has been demonstrated clearly in this study, and is due to the concentration of Gd-211 particles and presence of solidified liquid phase and impurities in these regions.
In summary, this study suggests that the observed trend in J c at different positions in the single grain GdBCO sample prepared using a buffer and additional liquid phase is significantly different to that observed for the size and concentration of RE-211 particles. In particular, there is no clear correlation between the distribution of RE-211 inclusions and local J c within the single GdBCO grain. The porosity of the sample, on the other hand, is a much more dominant factor in determining the distribution of J c than Gd-211 particles. The highest quality material occurs is at the centre of the top surface of the sample, whereas porosity at the centre and poor superconductivity at the edges of the single grain are responsible for the rapid decrease of the J c along the c-axis growth direction. The importance of porosity in controlling local critical current density suggests that process refinement aimed at reducing porosity may help improve the uniformity of J c within a single GdBCO grain.