The influence of porosity on the superconducting properties of Y–Ba–Cu–O single grains

The trapped field in Y–Ba–Cu–O (YBCO) bulk single grain superconductors correlates directly with the critical current density J c, which, in turn, is dependent on the microstructure of the bulk material. It has been shown recently and indirectly that porosity influences J c of these technologically important materials, in addition to the presence of well-researched Y2BaCuO5 (Y-211) particles in the bulk sample. In this work, we report the direct impact of porosity on the critical current density of a single grain YBCO bulk superconductor using 3D x-ray computer tomography scans and superconducting quantum interference device measurements. It is concluded that porosity has a considerably more substantial impact on the measured critical current density than Y-211 on the micrometre scale with, predictably, a decrease in porosity leading to an increase in J c. J c is directly proportional to the trapped field, so any method that can reduce porosity, therefore, improves J c, and, subsequently, the trapped field of these technologically important bulk superconductors.


Introduction
The trapped field of single grain, (RE)-Ba-Cu-O bulk superconductors [(RE)BCO, where RE = Y, Gd, Eu, Sm or Nd] is approximately ten times greater than the field generated by the alignment of spins in conventional ferromagnets. Indeed, a maximum trapped field of 17.6 T was measured in 2014 between two GdBCO(Ag) bulk superconductors reinforced * Author to whom any correspondence should be addressed.
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with stainless steel at 26 K [1]. The trapped field B trap in these technologically important materials is proportional to the product of the critical current density J c and the radius r of the bulk, single grain material (B trap ∝ J c ·r) [2]. According to Eisterer et al, the trapped field in Y-Ba-Cu-O (YBCO) bulk superconductors is unlikely to exceed 2.5 T at 77 K [3], although in practical materials the trapped field lies typically within the range of 0.7-1.1 T [4]. The significant difference between theory and the measured trapped field can be explained by the increased presence of pores, cracks and grain boundaries in the bulk microstructure with increasing diameter of the individual single grain. These defects limit significantly the integrity of the growth of a single grain to a few centimetres and, subsequently, decrease the macroscopic J c of the bulk sample [3].
As a result, the factors influencing J c must be investigated in order to increase trapped field. One such factor is the number and size of flux pinning centres in the single grain microstructure. The most effective flux pinning centres are characteristically nano-sized, non-superconducting defects or dopants within the superconducting (RE)Ba 2 Cu 3 O 7−δ (RE-123) phase matrix. Therefore, all inclusions that are larger than nanometre dimensions do not enhance flux pinning significantly. Consequently, and intuitively, the loss in superconducting volume leads to a reduction in J c [5].
The non-superconducting (RE) 2 BaCuO 5 (RE-211) phase has been investigated extensively as a main factor influencing J c . RE-211 forms along-side a liquid phase (Ba 3 Cu 5 O 8 ) and oxygen during the peritectic decomposition of RE-123, according to equation (1) [4] 2 (RE) The presence of a uniform distribution of nano-sized RE-211 second phase inclusions enhances J c of the bulk single grain [3]. However, the size of most RE-211 particles in the (RE)BCO single grain microstructure is typically within the range of 1-10 µm. Therefore, an excess of RE-211 inclusions reduces the superconducting volume, and hence the crosssection available to carry current rather than providing additional flux pinning centres. As a result, most of the flux tends to be pinned at nanometre sized dislocations and stacking faults at the RE-123/RE-211 interface [6,7].
A further factor influencing J c is the cross-sectional area of defects, which consists mainly of pores and cracks. Two kinds of pores can be found in (RE)BCO bulk superconductors: compaction and oxygen pores. Compaction pores have a typical size of between 1 and 10 µm and originate during the powder pressing stage of the green pellet prior to melt processing. Oxygen pores are larger, with a size of between 50 and 250 µm and result from the evolution of oxygen gas at elevated temperature during melt processing equation (1) [4].
Two distinct kinds of cracks are associated with these pores. Compaction cracks can expand vertically or horizontally throughout the entire sample [8], whereas small-scale, horizontally oriented cracks are usually the result of the tetragonal to orthorhombic phase transition that occurs during post-melt processing oxygenation [9].
Another negative influence on J c is the agglomeration of unreacted liquid phase equation (1) close to the edges of the single grain, which is both non-superconducting and does not pin magnetic flux.
An article discussing the influence of porosity on the critical current density and, subsequently, on trapped magnetic field has been published recently [5]. However, the correlation between porosity and critical current density has only been established indirectly by calculating the average J c from the measured trapped field with the formula published by Chen et al [10]. In this article, we investigate experimentally the direct effect of porosity on critical current density using x-ray computer tomography (XCT) and a superconducting quantum interference device (SQUID).

Fabrication of YBCO single grain
The single grain YBCO bulk superconductor studied here was fabricated from a powder containing 75 wt% Y-123 (Toshima, grain size: 2-3 µm, 99.9%), 25 wt% Y-211 (Toshima, grain size: 1-2 µm, 99.9%) and 0.5 wt% CeO 2 (Acros Organics, 99.9%). The powders were mixed using an electrical mortar and pestle for 2 h. About 40 g of powder was pressed into a green body precursor pellet using a 25 mm diameter die. The sample assembly for the single grain growth is shown in figure 1(a). Zirconia rods were coated with a suspension of Yb 2 O 3 (Alfa Aesar, 99.9%) in ethanol and placed on an alumina plate. The bottom surface of the green body precursor pellet was also coated with the Yb 2 O 3 suspension. The Yb 2 O 3 reacts with liquid phase (Ba 3 Cu 5 O 8 ) to form a protective layer of (Yb 2-x Y x )BaCuO 5 and a Yb-containing liquid phase that inhibits secondary grain nucleation from the zirconia support rods [11]. A YBCO buffer pellet was pressed and placed at the centre of the top of the precursor pellet [12,13] to prevent the diffusion of neodymium from the NdBa 2 Cu 3 O 7−δ (Nd-123) seed into the top layers of the YBCO bulk material. Neodymium contamination is known to decrease J c at the top surface of the bulk, YBCO single grain superconductor [14].
A single grain was processed using top-seeded melt growth (TSMG) [12]. The sample was heated at a rate of 60 • C h −1 from room temperature to 950 • C, maintained at this temperature for 2 h and then heated further at 50 • C h −1 to 1065 • C. The temperature was then decreased at a rate of 50 • C h −1 to 1025 • C after homogenisation for 1 h at 1065 • C and then decreased more slowly at 0.7 • C h −1 to 1012 • C, at 0.4 • C h −1 to 987 • C and at 0.3 • C h −1 to 980 • C before, finally, cooling to room temperature at a rate of 100 • C h −1 . The heating profile is shown in figure 1 The sample was annealed in flowing oxygen for 8-10 d at temperatures of 400 • C-450 • C to convert the structure of the as-processed Y-123 phase from tetragonal to superconducting orthorhombic.
The final bulk material had a diameter of 24.3 mm and a thickness of 12.8 mm due to shrinkage during growth, as shown in figure 1(c).

Measurements and microscopy
The top and bottom surfaces of the sample were polished for trapped field measurements using P600 grit polishing paper. An electromagnet was then used to apply a field of 1.2 T perpendicular to the ab-plane of the sample prior to field cooling to 77 K with liquid nitrogen. The magnetic field was then removed at a rate of 0.012 T s −1 and the maximum trapped field determined using a hand-held Hall probe positioned 0.5 mm above the sample surface. In addition, the quality of the sample was investigated by measuring the trapped field distribution with 18 rotating Hall probes positioned 1.5 mm above the ab-plane of the sample.
The sample was cut in half through the middle of a growth sector. One cross-section was polished to 1 µm using diamond paste. The cross-section of this half of the sample was imaged using an optical tracking microscope (OLYMPUS BX51M), and the images were assembled with the microscope software (LAS BX51M). The total area of defects, porosity, pore count, average pore size and pore size distribution were evaluated from the optical tracking microscope image using ImageJ software. Firstly, the image was converted to 8-bit, and the area of defects, including cracks, pores and liquid phase, was determined using the 'Auto Local Thresholding' method according to Sauvola and Pietikäinen [15]. Secondly, a threshold was set to mark and select pores manually for the determination of the cross-sectional porosity.
An optical microscope (NIKON ECLIPSE ME 600) was used with a Moticam camera to investigate the Y-211 particle size, count and concentration. Twelve images, 1 mm apart with an area of 80 × 60 µm were taken along the c-axis from the position immediately beneath the seed. The Y-211 particles were selected manually using ImageJ software and marked accordingly.
Specimens with an average size of 1.8 × 2.3 × 1.6 mm 3 (a × b × c) were cut from the remaining half of the sample, starting at the position immediately beneath the seed and moving down through the single grain along the c-axis to the bottom of the sample, as illustrated schematically in figure 2. T c and M-H loops of all eight specimens were measured using a SQUID (QUANTUM DESIGN MPMS 3 Magnetometer). A field of 2 × 10 −3 T was applied along the c-axis at 80 K for the measurement of T c . The temperature was then swept from 80-96 K and the M-H loop measured with a field sweep from 0-7 T at 77 K. T c , ∆T 90 and J c were determined for each specimen. ∆T 90 was calculated from the M-T measurements as the temperature difference between T c and the temperature at 90% of the minimum value of the magnetic field. J c was calculated for each specimen using the extended Bean model [16].
The volume porosities of all 8 specimens were determined using 3D XCT (ZEISS XRADIA VERSA 510) and evaluated using ImageJ software. The advantage of XCT is that the volume porosity of every specimen investigated in the SQUID can be measured precisely by evaluating stacks of 360-760 images with sufficient resolution to investigate the presence of oxygen pores and larger cracks (1 pixel = 3.38 µm). The image sequences were converted to 8-bit data and the default threshold method in ImageJ was used to mark the YBCO specimen cross-section on each image. Subsequently, the specimen areas in the images were measured once, including and once excluding holes with the ImageJ 'Analyze Particles' tool. The areas of all images were summed up and multiplied by the distance between the stacks (=1 pixel) to determine the volume with and without pores. The volume porosity was defined as the pore volume divided by the overall volume. This method was suitable for detecting cracks and pores in the sample microstructure.

Microstructural analysis of the YBCO bulk single grain
The cross-section of the YBCO bulk single grain of diameter 24.3 mm was imaged using an optical tracking microscope, as shown in figure 3. The overall area of defects was determined from these images to be 10.46%, of which 6.88% were pores. Pores were observed mainly at the centre of the sample with only isolated pores occurring towards the edges of the single grain. The oxygen evolving during the TSMG equation (1) has a shorter escape route towards the edges than that generated at the centre of the material. Consequently, oxygen is trapped predominantly in the form of pores at the sample centre.
The sizes of a total of 3753 observed pores were investigated using ImageJ software. Over 99% of the pores were sized between 30 and 250 µm, as shown in figure 4, which correlates well with the size distribution measured previously for the formation of pores due to the evolution of oxygen gas [4]. An average pore size of 85 µm was observed for the single grain YBCO sample in this study.
The residual 3.58% defects observed in the single grain microstructure can be attributed to the presence of cracks and unreacted liquid phase. Two distinct kinds of cracks  were found to occur parallel to the ab-plane, as shown in figure 3. Longer and thicker cracks are likely to result from the powder compaction process [8], whereas microcracks result from the tetragonal to orthorhombic phase transition during post-processing oxygenation [9]. The cracks are tilted by an angle of about 7 • -8 • , which, since they are parallel to the ab-plane, indicates that the ab-planes are slightly misaligned with the sample surface.
The bottom 1 mm of the material is not well defined, as shown in figure 3. Dark-in-contrast regions indicate the presence of residual, unreacted liquid phase from the TSMG process equation (1), and the presence of small miss-orientated secondary grains suggest multi-grain growth associated with non-optimal melt processing conditions.

Superconducting properties of the YBCO single grain
The trapped field profile of the YBCO bulk superconductor of 24.3 mm in diameter was measured at 77 K at a distance of 1.5 mm above the top and bottom surfaces of the single grain, as shown in figure 5.
The trapped field profiles measured at the top and bottom of the single grain both exhibit a conical shape with an increasing and decreasing field gradient for the top and bottom of the sample from its edge to its centre, respectively. No inhomogeneities, local maxima, or minima were observed in the trapped field profiles of either the top or the bottom of the single grain. The homogenous trapped field profiles demonstrate unequivocally that the single-grain growth was successful throughout the entire sample. Maximum and minimum trapped fields of 0.652 T and −0.443 T were measured with a hand-held Hall probe positioned 0.5 mm above the surface at the top and bottom of the sample, respectively. The difference of 0.209 T in the magnitude of trapped field suggests the presence of inhomogeneities within the sample microstructure.
A vertical column along the c-axis immediately beneath the seed was cut from the parent single grain and 8 specimens of approximate dimensions 1.8 × 2.3 × 1.6 mm 3 were, in turn, cut from this column, as illustrated in figure 2. T c , ∆T 90 and J c were determined for each specimen using a SQUID magnetometer. The T c of the specimen at the location immediately beneath the seed was measured to be the lowest (90.46 K). The T c increased along the c-axis until a maximum of 91.53 K was observed at a distance of 5.7 mm from the seed. The T c then decreased to 91.06 K at the bottom of the sample, as shown in figure 6. It should be noted that even the maximum T c   [17]. The highest Tc was measured at a distance of 5.7 mm from the seed (91.53 K). The value of ∆T 90 is relatively low for the first seven specimens (1.03-1.76 K) and reaches a maximum at the bottom of the single grain (9.7 mm, 4.62 K). measured in this study is lower than that of single crystal YBCO samples (92 K), indicating that impurities probably influence the T c of the sample.
A further indication of quality of a bulk superconductor is the value ∆T 90 . This value was relatively low for the first seven specimens (1.03-1.76 K). A maximum value of 4.62 K was determined for the specimen at the bottom of the bulk material (1 H, 9.7 mm distance from the seed), as shown in figure 6. The relatively high value of ∆T 90 at the bottom of the sample can be explained by the increasing agglomeration of non-superconducting, unreacted liquid phase and the growth of multiple grains towards the bottom of the bulk single grain.
M-H current loops were measured for each specimen to investigate the local and field-dependent behaviour of J c at 77 K, as shown in figure 7. The best performance at high field was observed for the specimen located immediately beneath the seed, which maintained a J c of 1.83 × 10 4 A cm −2 at 2.2 T. The lowest J c within the entire applied field range of 0-7 T was measured for the specimen furthest away from the seed (1 H, 9.7 mm), which can probably be attributed to the high concentration of unreacted liquid and secondary phase at the bottom of the sample. J c of the six specimens (1B-1G) cut from the centre of the single grain was similar over the entire measured field range.
The investigation of the superconducting properties reveals that the most significant changes in sample properties can be found close to the top and bottom surfaces of the sample. In contrast, only slight variations were observed in the central sections of the sample. The observed superconducting properties correlate well with the microstructural observations of the YBCO bulk single grain ( figure 3). Whereas only a few flaws are evident at the top of the sample, the bottom surface contains a significant concentration of unreacted liquid phase and evidence of multi-grain growth. The central region of the single grain, however, is characterised by a homogenous distribution of pores.

Microstructural factors influencing the critical current density
The distribution and size of Y-211 particles were investigated from the position immediately beneath the seed and along the c-axis towards the bottom of the single grain. Figure 8 shows an optical microscope image taken at a distance of 11 mm from the seed, which reveals the presence of dark grey Y-211 particles in a lighter grey-in-contrast matrix of the Y-123 phase. Black spots are an indicator of residual liquid phase and white particles suggest a fine distribution of CeO 2 .
The measured size of the Y-211 particles, with an average of 0.94 µm, is constant within experimental error for the whole sample, as shown in figure 9(a). The overall Y-211 content increases from 7.8% to 37.0% from the top to the bottom of the sample, as shown in figure 9(b). These results correlate well with particle-pushing theory and previous studies on the properties of RE-211 particles [18][19][20][21][22]. According to Murakami et al, J c increases with Y-211 particle volume, V 211 , divided by Y-211 particle size, d 211 (J c ∝ V 211 /d 211 ) [23]. We would expect, therefore, an increase in J c along the c-axis since d 211 remains constant within experimental error and V 211 increases towards the bottom of the single grain. However, the opposite trend in J c was observed, in this study, as shown in figure 7. Other authors have also observed this effect [8,24,25]. It can be concluded, therefore, that additional factors must influence the critical current density in bulk, single grain YBCO superconductors.
The volume porosity was determined from XCT-scans of all eight specimens measured by SQUID-magnetometry. One representative XCT-image close to the surface of the ab-plane  is shown in figure 10 for each specimen. It is evident that the level of contrast and resolution (1 pixel = 3.38 µm) in the images is sufficient to detect pores. The image of the specimen directly beneath the seed (1A) shows neither pores nor inhomogeneities, whereas specimens 1B to 1G are clearly porous. The bottom specimen contains only a few pores but exhibits a black stripe, which is likely to correspond to the presence of unreacted liquid phase ( figure 10(1H)). Very few cracks were observed in the XCT-images of the specimens investigated.
The area with and without pores was evaluated for 360-760 images and multiplied by the slicing distance (=3.38 µm) for each specimen. The percentage difference between the volume without and with pores represents the volume porosity. The volume porosity is likely to be relatively precise due to the large number of images analysed for each specimen. The position of each specimen was plotted against the area of defects determined from the XCT-scan images and the measured J c (77 K, 1 T) in order to compare these two properties throughout the sample, as shown in figure 11. It was observed for the first seven specimens that an increase in the area of defects correlates directly with a decrease in J c . Similar observations have been made previously for GdBCO single grain bulk superconductors [8].  Correlation between the area of defects and Jc (1.0 T) at 77 K. The point indicated in red is the specimen at the bottom of the sample (9.7 mm) and is influenced by multi-grain growth and an increased presence of unreacted liquid phase [17].
The area of defects and J c appear to be indirectly proportional, which can be observed more clearly by plotting the area of defects against J c (77 K, 1.0 T), as shown in figure 12. The data point at the bottom of the sample (9.7 mm) is indicated in red, since secondary grain growth and the presence of an increased concentration of unreacted liquid phase appear to have a more pronounced effect on the properties than pores on the measured J c of this specimen.

Conclusions
The microstructural properties influencing J c and, subsequently, the trapped field (B trap ∝ J c ·r) were investigated in a bulk, single grain YBCO superconductor. It is concluded that porosity has a significantly greater impact on the critical current density than the presence of Y-211 particles. The presence of grain boundaries and unreacted liquid phase have an even more substantial effect on limiting J c towards the edges of the single grain. Understanding the factors that influence J c can help improve the processing of (RE)BCO bulk superconductors and lead to higher trapped fields in these technologically important materials.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.17863/ CAM.95715 [17].