Superconducting joints of reacted monofilament MgB2 wires sintered by hot uniaxial pressing system

Successful superconducting joints of reacted magnesium diboride (MgB2) monofilament wires are reported in this paper. The absence of a reliable method to develop superconducting joints between reacted MgB2 wires presents a major obstacle to the wider adoption of MgB2 as a material for magnet winding. A hot uniaxial pressing (HUP) system was exploited for sintering purposes since it can facilitate the formation of condensed in situ bulk on the wire filament. The wires were manufactured with an extra thick barrier material to protect the filament from damage during HUP sintering. The sintering temperature and pressure of the HUP system were varied to comprehend the best-performing joint. The performance of joints could be improved by depreciating the pores within the intermediate bulk of the joint. To prove this point, joints were cut to study their morphology. However, due to sintering in pressurised conditions, the reaction of the in situ intermediate bulk was not completed. The x-ray diffraction result detected a significant unreacted magnesium phase in the intermediate bulk. This work obtained joints of reacted MgB2 wires which can be considered for industrial MgB2 magnetic resonance imaging magnets fabrication.

Successful superconducting joints of reacted magnesium diboride (MgB 2 ) monofilament wires are reported in this paper.The absence of a reliable method to develop superconducting joints between reacted MgB 2 wires presents a major obstacle to the wider adoption of MgB 2 as a material for magnet winding.A hot uniaxial pressing (HUP) system was exploited for sintering purposes since it can facilitate the formation of condensed in situ bulk on the wire filament.The wires were manufactured with an extra thick barrier material to protect the filament from damage during HUP sintering.The sintering temperature and pressure of the HUP system were varied to comprehend the best-performing joint.The performance of joints could be improved by depreciating the pores within the intermediate bulk of the joint.To prove this point, joints were cut to study their morphology.However, due to sintering in pressurised conditions, the reaction of the in situ intermediate bulk was not completed.The x-ray diffraction result detected a significant unreacted magnesium phase in the intermediate bulk.This work obtained joints of reacted MgB 2 wires which can be considered for industrial MgB 2 magnetic resonance imaging magnets fabrication.

Introduction
Nowadays, a low-temperature superconductor (LTS) niobiumtitanium (NbTi) is commercially used for manufacturing the superconducting magnet of the magnetic resonance imaging (MRI) system.MRI systems have been widely installed all over the world to be an effective and efficient method of diagnosis [1].However, the liquid helium (LHe) source is critical for the operation of these magnets of LTS due to its low critical temperature (T c ). LHe is a finite resource with steeply increased prices in the recent decade [2].Therefore, a replacement of LTS magnets should be considered.Magnesium diboride (MgB 2 ) with a T c of 39 K has always been considered a potential candidate as a next-generation material for superconducting magnets [3][4][5][6][7].ASG superconductors have developed the 'MROpen Evo' system which uses MgB 2 as the material of the superconducting magnet [5].Hitachi has also developed an MRI system with an MgB 2 magnet which is capable of rapid generation of a magnetic field [6].The magnet of the 'MROpen Evo' system does not operate in the conventional persistent mode to generate a stable magnetic field (decay rate less than 0.1 ppm h −1 ) for imaging purposes [8]. Figure 1 demonstrates a superconducting magnet operates in the persistent mode.The coils are connected in a modular fashion to achieve the desired magnetic field and reduce the required length of superconducting wires [9].A persistent current switch is connected to short-circuit the coils after charging the system with the power supply [10].Therefore, superconducting joints are critical for MRI magnet manufacturing.
The superconducting joints of MgB 2 conductors have been reported to be fabricated with both monofilament conductors [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and multifilament conductors [3,4,8,11,14,[29][30][31][32].Only a few of these articles reported the performance of joints of reacted MgB 2 conductors [11,20,30].Current technology of MgB 2 magnet fabrication necessitates the winding of coils using unreacted wires followed by sintering.This technique suffers from drawbacks that increase manufacturing costs with high scrap rates.The lack of technology related to joining reacted superconductors makes it impossible to repair the magnets due to joint failure.Therefore, developing an effective technique for joining reacted MgB 2 conductors is a critical part of the MRI application [7,33].To solve the difficulty of joining reacted MgB 2 filament, Oomen have presented their joints of reacted multifilament MgB 2 wires by hot pressing [34].They have demonstrated a condensed microstructure that does not exhibit cracks at the joining interface between the wire and the intermediate bulk, but the retained I c of the joint compared to the unjoined wire was only 25% in 1 T [34].Improving this I c retention rate (CCR, calculated by dividing the I c of the joint by the I c of the unjoined wire as a percentage [9]) is vitally important.This work gave us insight into the potential of the application of the hot uniaxial pressing (HUP) system for joints of reacted MgB 2 wires fabrication.HUP system is found to be effective for improving the intrinsic connectivity and the critical current density (J c ) of an MgB 2 bulk up to twice the ones pressed in room temperature conditions [35][36][37].The scanning electron microscopy (SEM) images published related to MgB 2 joints have revealed that the connection between the conductor and the intermediate bulk is affected by the porous structure of the bulk [4,32].Therefore, we believed that by manipulating the condition of HUP, the interface could be further improved to demonstrate a higher I c retention rate.
In this work, a total number of six joints with various conditions were fabricated with the HUP system.Different temperatures and pressures were adopted to find the optimised sintering condition for joints of reacted monofilament wires, so the highest I c values could be found.The joint was fabricated to have the structure of a 'Termination Joint' which has its two wires joined by an intermediate bulk [9].This structure is appropriate for the HUP system since the pressure can be applied effectively on the intermediate bulk without damaging the exposed wires during sintering.To justify their performance, transport I c and T c measurements were conducted.In addition, SEM, energy dispersive spectroscopy (EDS), and x-ray diffraction (XRD) were conducted on selected samples to understand the microstructure and composition of the samples.

Experiment procedure
The fabrication of joints includes two sections.Firstly, the monofilament wires were fabricated and prepared for joining.Then, joints of reacted wires were manufactured by HUP.The performance of the joints (I c and T c ) was measured by a cryocooler at various conditions.XRD analysis was conducted to determine the phases in the joints.SEM and EDS were used to observe the microstructure of the joining section and obtain the elemental mapping to justify the interface between the wire and the intermediate bulk.

Wires fabrication and preparation
The magnesium powder (abcr, 99.8%, −325 mesh,) and boron powder (Pavezyum, amorphous, nano boron) were first mixed in a ball mill for 40 min in an argon (Ar) environment.This mixture of powder was used for the entire study.The wires were fabricated by powder in tube method (the tube and hot extrusion machine photos can be found in the supporting document).The Mg + 2B powder was filled in a niobium (Nb) tube (acting as the barrier material) which was later inserted into a copper-silver (Cu-Ag) tube (acting as the sheath material).The wires were fabricated by hot extrusion and swaging of the filled tube.The entire filled tube was first extruded to a diameter of 5 mm and then swaged to 2 mm.After swaging, the diameter of the Nb barrier was decreased to approximately 1.2 mm and the inner diameter of the mixture was around 0.5 mm (filling factor: 6.25%).Other than the conventional function of the Nb barrier (prevent reaction between Mg and Cu), it was also designed to be thick (∼0.35 mm) to protect the brittle MgB 2 filament from damage caused by both pressing at room temperature and the HUP system.The wires were sintered in a box furnace (Brand: neoterm Model: NT1313 Series X) at 650 • C for 1 h in an Ar environment.The temperature was increased at a rate of 10 • C per minute and the wires were cooled inside the box furnace in an Ar environment until room temperature (Approximately 8 h).A crosssectional drawing of the sintered wire is shown in figure 2(a).The sintered wires were etched with nitric acid (65% w/w) for 30 min to remove the Cu-Ag barrier material, so it would not react with the in situ powder during joining [18].Finally, the etched part of the wire was cut at an angle of 30 • angle to increase the exposed area to improve the joining interface (shown in figure 2(b)).

Joint fabrication
The schematic drawings of each step of joint fabrication are shown in figure 2. The mould design is already reported in previous articles [3,4,8,12,17,18,32,38].The reacted wires and the mould were moved in a glove box (Ar gas environment) for joint manufacturing.The mould of intermediate bulk was first filled with 0.1 g of the mixed Mg + 2B powder, followed by applying a pressure of 225 MPa.This preliminarily filled mould was taken out of the glove box in the open air to insert the reacted wires.Sealing material (SOUDAL, oven sealant, sodium silicate) was applied on the opening of holes for wire insertion and the sealant was allowed to dry for 24 h.Thus, wires can be mounted properly to prevent risks of bending and damage before applying more pressure.The mould with the inserted wires was again moved into the glove box for subsequent manufacturing.More mixed powder (0.65 g) was filled inside the mould to cover the exposed wires and act as an intermediate bulk to provide the connection between the two wires.A pressure of 45 MPa or 112.5 MPa was applied to the filled powder to form a condensed bulk at room temperature.The selected 112.5 MPa is considered to be the maximum pressure that can be applied without damaging the wires.The mould with the wires was taken out of the glove box to apply sealing material.The sealant was utilised on all the openings to prevent oxidation and Mg evaporation during heat treatment, and it was allowed 24 h for drying.The sample was inserted into the chamber of the HUP with a pressure of 13.78 or 20.66 MPa.The pressure was applied on the intermediate bulk to improve the intergranular connectivity and depress porosity.The temperature of the sintering was set to be 650 • C, 675 o C and 700 o C for 4 h with a ramping ratio of 15 • C per minute.The pressure was maintained for the entire sintering process in an Ar gas environment.After sintering, the sample was cooled naturally inside the chamber with the same pressure for another 12 h before the sample was ready for measurements.The joints were pressurised during cooling since we would like to minimise the effect of thermal expansion to prevent any possible displacement of the wires.Six samples were manufactured, and details are listed in table 1.
The pressure selection for the HUP system is much lower than the room temperature pressure.The hot pressure is applied to facilitate the formation of the MgB 2 phase on the surface of the reacted wires.The complete bulk reaction between the in situ powder and the MgB 2 filament of the wire is unrealistic since the MgB 2 filament will be quite stable under the reaction temperature of in situ Mg + 2B powder.Thus, the HUP system is critical for the formation of a condensed MgB 2 phase on the top of the filaments.Instead of a complete reaction, the HUP system can reduce the porous volume during the bulk formation and ensure better connectivity at the desired in situ precursor reaction temperature.The volume of the HUP processed bulk will be further reduced and improve the joining interface.However, if improper hot pressure is selected, the inserted reacted wires can be damaged due to deformation caused by volume shrinkage.

Measurement and microstructural analysis procedure
The sintered joint was first mounted in a test probe (figure 2(i)) and a temperature sensor was attached close to the joint.The four-probe measurement setup was used for both I c measurement and T c measurement.The 1 µV cm −1 criteria were utilised to justify the I c of each joint.The distance between the voltage probes is 2 cm (defined by the length of joined wires between the voltage probes), so the measured voltage data was divided by 2 cm to obtain the electric field and fit the criteria.T c was measured by the heating process by passing 1 mA constantly.Microstructural analysis was carried out after cutting the joints to expose the joining interface.The images of microstructures were taken by the ZEISS Ultra Plus SEM machine, and elemental mappings were acquired by EDS using the same machine.The intermediate bulk was taken out of the joint and ground into powder for phase identification.The Smartlab 3 kW x-ray powder diffractometer Rigaku machine was used for XRD analysis.

Superconducting property
The result of the I c values of each joint in self-field is plotted in figure 3.Among all joints, Joint 1 showed the highest I c value at all temperatures which are 47.6 A, 47.3 A, 40.3A and 30.1 A at 12 K, 15 K, 20 K, and 25 K, respectively.Thus, the HUP condition of 650 • C for 4 h with 13.78 MPa and 45 MPa before HUP is the best sintering method reported in this article.This high I c value can be improved by better intergranular connectivity between the wires and the intermediate bulk.
Joints 2 and 6 showed almost identical performance from 12 K to 20 K. Compared to Joint 2, Joint 6 is less sensitive to the increase in temperature (from 20 K to 25 K), its I c was about 2.95 A higher than Joint 2 at 25 K. Joint 4 reached the lowest performance among all the joints which can be caused by poor connectivity between the wires and the intermediate bulk.In addition, the I c performance of Joint 5 was missing since the joint was resistive during measurement.This could have been caused by wire damage during the HUP process.The I c performance of the wire sintered at 650 • C for 1 h was tested in various temperatures and the results are shown in figure 3. The highest I c value of the wire is 68.3A at 12 K.However, this set of data cannot be used for the calculation of CCR values of the joints, because the sintering condition of the wires is different from the joints.To calculate the CCR values, the wires should be sintered with the exact conditions as the corresponding joints (650 • C for 1 h followed by the sintering condition of each joint).We could not measure the performance of doublesintered wires due to the depression of I c performance caused by dual sintering.The CCR value is a significant parameter to determine the performance of a superconducting joint.Thus, we will investigate the retention mechanism in the future.Figures 4(a)-(c) show the electric field versus current curves of Joints 1, 2 and 6.As discussed in the previous section, Joint 1 is the best-performing sample.Comparing figures 4(a) and (b), the transition of Joint 1 is observed to be steeper compared to Joint 2. Based on the equation for n-value calculation (V = V c (I/I c ) n ), where V is the voltage, V c is the voltage at I c , I is the current and n is the n-value), a steep transition will increase the n-value of the joint which will eventually enhance the operation current in the MgB 2 magnet fabricated with this joining method [39,40].The n-value(s) of Joints 1, 2 and 6 in self-field are shown in table 2. Joint 1 not only retained the highest I c value but was also estimated to have the highest n-value(s) of 38.30 and 57.93 at 12 K and 15 K, respectively.Joints 2 and 6 showed almost identical I c performance from 12 K to 20 K in self-field, but from figures 4(b) and (c), Joint 6 displays a much steeper transition compared to Joint 2 which leads to higher n-value(s) at all temperatures.Despite the similar I c performance of Joints 2 and 6, the much higher n-value(s) of Joint 6 predicted higher operational current in persistent mode operation.In addition, the n-value of Joint 6 was slightly higher than Joint 1 at 20 K, but the I c of Joint 6 was much lower.Therefore, it can be anticipated  that the persistent mode operation of Joint 1 will still outperform Joint 6.However, all these n-value(s) were estimated in self-field which is not suitable for the persistent mode operation.Further investigation towards in-field measurements of samples is critical.and (c).The microstructure of the intermediate bulk of Joint 6 is observed to be more porous than Joint 1. Higher pressure was applied to Joint 6 in both room temperature and HUP system, however, a more porous microstructure was obtained.In figure 5(c), pores of the bulk have formed on the surface of the wire which has affected the connectivity of the joint.The pore size of the bulk Joint 1 is much less than 100 µm which makes it almost impossible to measure under 200 times magnification.However, the interface formation of both joints is quite consistent.No obvious difference in the microstructure of bulks and wires can be observed.By further increasing the magnification to 500 times, figures 5(b) and (d) revealed more details of the interface.In figure 5(b) the interface line of Joint 1 is clearer and its trend has been marked by the yellow line.
The difference between the microstructure of the wire filament and the bulk is also enhanced.The wire filament of Joint 1 exhibited a more porous structure compared to its bulk since  the wire had been sintered before the HUP process.Thus, its microstructure is not as condensed as the bulk.Although the magnification has been increased to 2.5 times, the pores of the bulk are still minor.On the other hand, in figure 5(d), the phenomenon of pores formation on the interface area is also proven.To further investigate Joint 1, the magnification was increased to 1000 times and 2000 times in figures 5(e) and (f).
In these figures, a large number of small crystals were detected by the SEM.These crystals were filled inside the pores of the bulk which made it difficult to observe any pores at low magnification.The existence of the small crystal phases can act as flux pinning centres which can potentially improve the performance of Joint 1 in a magnetic field.Figure 5(g) focuses on the wire part and figure 5(h) is the bulk side.Comparing these two images, the bulk side has more crystal phase.It can be predicted that the occurrence of the crystal phase is caused by the HUP procedure and broken pieces during the cutting and polishing of the sample.The identification of these crystal phases can be determined later in EDS and XRD analysis.These SEM images confirmed the feasibility of fabricating joints of reacted MgB 2 wires by the HUP system.By applying appropriate sintering pressure and temperature, MgB 2 can be formed on the surface of the reacted wire filament to successfully achieve superconducting joints.However, the existence of the small crystals cannot be the reason for the better connectivity of Joint 1, but it can prove its high packing density.[41].The increment of the melting point could have affected the formation of MgB 2 .The temperature applied for Joint 1 was only 650 • C for 4 h which did not reach the temperature for Mg to transform from solid phase to liquid phase.The idea of incomplete reaction was endorsed by the XRD result.From figure 6(f), the highest intensity detected was the Mg phase which is 67.2 mol % whereas MgB 2 is only 27.7 mol %.The high mole percentage of the Mg phase proved that the crystal observed in SEM images was an unreacted Mg phase.To further prove the concept of low reaction temperature, Joint 3 was also tested.In figure 6(f), the major phase of Joint 3 (reacted at 675 • C with the same pressing condition) was MgB 2 (∼87.27mol %) which was much higher than Joint 1 and its unreacted Mg phase was decreased to only 3.53 mol %.This XRD result has confirmed that the sintering temperature of Joint 1 was not sufficient for a complete reaction.Moreover, the content of oxygen (O) of Joint 1 is shown in figure 6(e), this impurity could have been induced when the wires were inserted into the mould.Some Mg + 2B powder was sticking on the surface of the wire and introduced this impurity.Besides, during the HUP process, the sealing material was crushed by the pressure.Although Ar gas flow was maintained throughout the entire heating and cooling process, some O could have contaminated the powder.Moreover, the MgO could also be formed during the first drying process in open air [4,7,42].In the XRD analysis of Joints 1 and 6, 5.1 and 9.03 mol % of MgO were detected, respectively.The higher sintering temperature of Joint 3 not only increased the content of MgB 2 but also induced more impurity MgO phase.

Conclusion
Joints of reacted MgB 2 monofilament wires were successfully manufactured by using the HUP system.The best joint (Joint 1) was first pressed by 45 MPa at room temperature and 13.78 MPa in the HUP system.The joint was sintered for 4 h at 650 • C in an Ar environment with the pressure applied during the entire sintering process.It reached an I c (s) of 47.6 A, 47.3 A, 40.3A and 30.1 A at 12 K, 15 K, 20 K, and 25 K, respectively.The T c of all joints fabricated are similar which are in the range from 33.5 K to 35.2 K. SEM images of Joints 1 and 6 were compared.Joint 1 had a condensed microstructure with fewer pores formed on the interface of the joint.However, many crystals were also detected from the SEM analysis which were filling the pores of the joint.These crystals could contain broken pieces of the sample from polishing and unreacted Mg.The existence of an unreacted Mg phase was further proven by the elemental mapping from EDS and phase identification from XRD.The Mg phase was discovered to be 67.2 mol %.The increased temperature of transformation from solid state Mg to liquid state Mg due to pressure can be the cause of this incomplete reaction.This is a preliminary work of joint fabrication using the HUP system.In future, the CCR values of joints fabricated in this work should be investigated and they should be measured in various magnetic fields (for I c and n-value) to examine the feasibility of MRI magnet applications.Additionally, for further improvement, the unreacted Mg phase should be decreased to improve the performance.

Figure 1 .
Figure 1.Schematic illustration of an MRI magnet operating in persistent mode.

Figure 2 .
Figure 2. Schematic drawings of the manufacturing process and photographs of the wire cross-section, a sintered joint and the test probe for Ic and Tc measurement.(a) A photograph of the cross-section of the wire.(b)The sintered wires were etched to remove the Cu-Ag barrier and cut at an angle.(c) Mg + 2B powder was first filled in the mould and pressed at room temperature in a glove box.(d) Wire insertion and application of sealant.(e) More powder was filled, and less pressure was applied to the glove box.(f) More sealant was applied to the top opening.(g) A schematic drawing of the HUP system (details are shown in the supporting document).(h) A photograph of a joint after HUP.(i) The test probe in the cryostat system with the indication of four probes used for measurement.

Figure 3 .
Figure 3.Comparison of Ic of different joints and the wire in self-field.

Figure 4 (
d) displays the resistance versus temperature plot.T c values of Joints 1, 2 and 6 are quite close which are 34.4K, 34.8 K and 33.8 K.The T c results of Joints 3 and 4 are shown in the supporting document.

3. 2 .
MicrostructureJoints 1 and 6 were cut to investigate the difference in joining interface by SEM since these are the two best-performing samples.Both joints were cut along one of the inserted wires to observe the connection.SEM images are shown in figure5.The interfaces of Joints 1 and 6 are magnified 200 times in the SEM and the microstructures are shown in figures5(a)

Figure 5 .
Figure 5. SEM images of Joints 1 and 6.(a) Interface of Joint 1 at 200 times magnification.The interface line has been circled.(b) An image of Joint 1 at 500 times magnification.A yellow line is drawn to separate the wire filament and the bulk.(c) Image of Joint 6 at 200 times magnification with the interface area circled by a yellow circle and the pores circled by white circles.(d) Joint 6 interface at 500 times magnification and the pores are circled by a white circle.(e) An image of Joint 1 interface area at 1000 times magnification.(f) to (h) Images of Joint 1 at 2000 times magnification at different locations.(f) and (g) Interface.(h) Bulk.

Figure 6 .
Figure 6.EDS images and XRD pattern of Joint 1 and XRD pattern of Joint 3. (a) The SEM image of the area selected for EDS of Joint 1.(b) Complete elemental mapping of Joint 1. (c) Mapping of Mg of Joint 1.(d) Mapping of B of Joint 1. (e) Mapping of O of Joint 1. (f) XRD analysis result of the bulk of Joint 1 and Joint 3 with unreacted Mg, MgB 2 and MgO phases identified.

Figure 6 (
Figure 6(a) indicates the SEM image of the area selected from Joint 1 for EDS mapping.Figure 6(b) is the overall elemental mapping with Mg, B and O plotted on the SEM image of Joint 1. Comparing figures 6(c) and (a), the Mg was mostly detected at the centre of the joint.Many crystals could be observed in this area which can be expected to contain not only broken pieces of the sample but also some unreacted Mg which formed small crystals in the intermediate bulk.To prove this, figure 6(d) was compared to figure 6(c), the density of B (green) points is much lower at the Mg area.The large amount of Mg did not completely react with B during the sintering.

Figure 6 (
Figure 6(a) indicates the SEM image of the area selected from Joint 1 for EDS mapping.Figure 6(b) is the overall elemental mapping with Mg, B and O plotted on the SEM image of Joint 1. Comparing figures 6(c) and (a), the Mg was mostly detected at the centre of the joint.Many crystals could be observed in this area which can be expected to contain not only broken pieces of the sample but also some unreacted Mg which formed small crystals in the intermediate bulk.To prove this, figure 6(d) was compared to figure 6(c), the density of B (green) points is much lower at the Mg area.The large amount of Mg did not completely react with B during the sintering.The melting temperature of Mg could have been increased from 650 • C to approximately 660 • C under a pressure of 13.78 MPa according to an Mg phase transformation diagram composed by Errandonea et al[41].The increment of the melting point could have affected the formation of MgB 2 .The temperature applied for Joint 1 was only 650 • C for 4 h which did not reach the temperature for Mg to transform from solid phase to liquid phase.The idea of incomplete reaction was endorsed by the XRD result.From figure6(f), the highest intensity detected was the Mg phase which is 67.2 mol % whereas MgB 2 is only 27.7 mol %.The high mole percentage of the Mg phase proved that the crystal observed in SEM images was an unreacted Mg phase.To further prove the concept of low reaction temperature, Joint 3 was also tested.In figure6(f), the major phase of Joint 3 (reacted at 675 • C with the same pressing condition) was MgB 2 (∼87.27mol %) which was much higher than Joint 1 and its unreacted Mg phase was decreased to only 3.53 mol %.This XRD result has confirmed that the sintering temperature of Joint 1 was not sufficient for a complete reaction.Moreover, the content of oxygen (O) of Joint 1 is shown in figure6(e), this impurity could have been induced when the wires were inserted into the mould.Some Mg + 2B powder was sticking on the surface of the wire and introduced this impurity.Besides, during the HUP process, the sealing material was crushed by the pressure.Although Ar gas flow was maintained throughout the entire heating and cooling process, some O could have contaminated the powder.Moreover, the MgO could also be formed during the first drying process in open air[4,7,42].In the XRD analysis of Joints 1 and 6, 5.1 and 9.03 mol % of MgO were detected, respectively.The higher sintering temperature of Joint 3 not only increased the content of MgB 2 but also induced more impurity MgO phase.

Table 1 .
Conditions of samples.The pressures applied on each sample were calculated based on the dimensions of the joints and the size of the pistons of each press.

Table 2 .
The n-value(s) of Joints 1, 2 and 6 at different temperatures in self-field.