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M.A. Grigoroscuta, G. Aldica, I. Pasuk, M. Burdusel, V. Sandu, A. Kuncser, [T.S. Suzuki](https://orcid.org/0000-0001-9458-6863), [O. Vasylkiv](https://orcid.org/0000-0002-5041-6130), P. Badica

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This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1016/j.materresbull.2020.111103[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

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[Partially-oriented MgB2 superconducting bulks with addition of B4C and cubic BN obtained by slip casting under high magnetic field and spark plasma sintering](https://mdr.nims.go.jp/datasets/77451592-1e70-4619-a713-cf5f3b5d46d0)

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Enhanced MgB2 with Ga/In acetylacetonate additions using SPS techniquePartially oriented MgB2 superconducting bulks with addition of B4C and cubic BN obtained by slip casting under high magnetic field and spark plasma sintering M. A. Grigoroscuta1, G. Aldica1, I. Pasuk1, M. Burdusel1, V. Sandu1, A. Kuncser1, T.S. Suzuki, O. Vasylkiv2, P. Badica1*1 National Institute of Materials Physics, Street Atomistilor 405A, 077125 Magurele, Romania2 National Institute for Materials Science, 1-2-1 Sengen, 305-0047 Tsukuba, Ibaraki, JapanCorresponding author:P. BadicaNational Institute of Materials Physics, Atomistilor 405A, Magurele, Ilfov, 077125, Romaniaemail: badica2003@yahoo.comfax: +40-213690177ph: +40-21-3690185Submitted to J. Eur. Ceram. Soc.Partially oriented MgB2 superconducting bulks with addition of B4C and cubic BN obtained by slip casting under high magnetic field and spark plasma sintering M. A. Grigoroscuta1, G. Aldica1, I. Pasuk1, M. Burdusel1, V. Sandu1, A. Kuncser1, T.S. Suzuki, O. Vasylkiv2, P. Badica1*1 National Institute of Materials Physics, Street Atomistilor 405A, 077125 Magurele, Romania2 National Institute for Materials Science, 1-2-1 Sengen, 305-0047 Tsukuba, Ibaraki, JapanAbstractDense discs with starting compositions (MgB2)0.99(B4C)0.01 and (MgB2)0.99(c-BN)0.01 were fabricated by slip casting under a magnetic field H0 (perpendicular on the surface of the disc) of 12 T and subsequent spark plasma sintering. As-processed bulk material shows (00l) partial orientation of the MgB2. The degree of orientation is about 13 and 9 % when using B4C and c-BN additives. From magnetic measurements with magnetic field H parallel and perpendicular to H0, superconducting parameters were extracted and they present anisotropy. The maximum values of high field critical current density Jc and irreversibility field µ0Hirr are for H//H0 and these values are higher or similar than for randomly oriented samples. For the same orientation the critical temperature at midpoint Tc, mid of transition is slightly lower and suggests an anisotropic influence of carbon substituting for boron in MgB2. The volume pinning force Fp, max and Tc, mid are lower in the partially than in randomly oriented samples. The pinning-force-related parameters depend on the additive and orientation and establishing the major pinning mechanism based on them within scaling and percolation models is not reliable. A method to scale the normalized volume pinning force vs. reduced magnetic pinning force is proposed by involving a Gauss function: for the randomly oriented samples a single Gauss function works well, while for partially oriented samples (regardless H//H0 or HH0) a double Gauss function was necessary since in these samples a second maximum in Fp occurs.                   Keywords: MgB2, B4C and c-BN additions, critical current density, pinning force, c-axis texture 1. IntroductionSuperconducting properties of MgB2 are widely investigated in relation with additions, microstructures, and processing technologies. It is noteworthy that indicated factors are not independent and one has to pay attention to their synergetic and complex nature. In general, a high density and nanostructured material is necessary to achieve enhancement of the flux pinning, of the critical current Jc, and of the irreversibility field µ0Hirr.  Higher Jc and µ0Hirr values can boost applications of MgB2 with significant commercial impact. In our work, we have prepared high density bulk samples of MgB2 by spark plasma sintering (SPS) [noi Phys C primul]. The route we apply is defined in literature as ex situ, i.e. the raw material is the powder of the MgB2 compound. In the in situ routes, two powders that contain separately Mg and B are the raw materials and MgB2 forms by chemical reaction between Mg and B. We tested different additions [noi carte 2017]. For our technology, among the most efficient for improvement of the superconducting parameters were B4C [noi Mater Res Bull] and cubic BN (c-BN) [noi SUST].Recently, we successfully fabricated partially c-axis oriented pristine MgB2 bulk samples [noi SUST orient1]. The texture of MgB2 was obtained by combining slip casting under a high magnetic field of 12 T and further SPS processing. Our promising results enable continuation of the studies targeting improvement of the superconducting functional parameters such as Jc and Hirr by taking advantage of the anisotropic nature of MgB2. The details of pinning in textured MgB2 bulk also deserves attention. Hence, fabrication and characterization of partially textured MgB2 bulks with additives is the next natural course of investigation and this is the aim of this work. The criteria for selection of the additives, B4C and c-BN, are not only their positive influence on pinning, Jc, and µ0Hirr as already mentioned in the previous paragraph, but also the fact that B4C is anisotropic (rhombohedral) and it was demonstrated that it can be aligned by magnetic slip casting [?? de cautat], while c-BN is isotropic (cubic).            2. ExperimentalRaw powders were MgB2 (Alfa Aesar, 99.5%, metals basis purity), B4C (Sinopharm, ?? Oleg/Mihai) and c-BN (???Oleg/Mihai). They were mixed and composition was (MgB2)0.99(A)0.01, where A denotes the additive B4C or c-BN. The starting composition was set based on our previous studies: (MgB2)0.99(A)0.01, A = B4C or c-BN is the optimum composition to maximize Jc and µ0Hirr [noi B4C, c-BN]. Powder mixtures were processed by magnetic (H0 = 12 T) slip casting and details are presented in ref. [17 din noi SUST orient1]. In the slip casting process, as a dispersing agent, the polyethyleneimine (PEI) (molecular weight = 10000, Wako Pure Chemical Industries Ltd., Japan) was used. The as-fabricated green bodies were loaded into a graphite mold system and SPSed by using a FCT Systeme GmbH – HP D5 (Germany) furnace. The SPS temperature was 1150 C for a dwell time of 30 min. The heating rate was 110 C/min. The maximum uniaxial pressure applied on the sample was P = 95 MPa. The direction of P coincides with direction of H0 used in magnetic slip casting processing. Discs of ~20 mm in diameter and 4 mm thickness were obtained. Reference samples (‘b’ and ‘d’ in Table 1), randomly oriented and with composition (MgB2)0.99(A)0.01, A = B4C or c-BN, were prepared by SPS for 3 min. These samples were not subject of high field slip casting (HFSC).The apparent densities ρaSPS (Table 1) of sintered discs were measured by Archimedes method. The theoretical densities ρtSPS of the composites were determined [18 din noi SUST orient1] considering the X-ray diffraction (XRD) patterns and the weight fraction (Table 1) of MgB2 (2.63 g/cm2), MgO (3.58 g/cm2), and MgB4 (2.49 g/cm3) phases obtained from Rietveld simulations (MAUD 2.31 [19 din noi SUST orient1]). The c-BN additive does not react with MgB2 [noi SUST], while B4C reacts with MgB2 during SPS processing.  [noi Mater Res Bull]. Phases c-BN and residual unreacted B4C (<1.3 wt. %) were not included in Rietveld analysis and in calculation of the theoretical density. The relative densities RSPS (%) were estimated with formula: RSPS=ρaSPS / ρtSPS x 100 (Table 1). XRD patterns were measured with Bruker AXS D8 Advance diffractometer (CuK radiation). The a and c lattice parameters of MgB2, the crystallite size for different phases, and the residual micro strain were determined by Rietveld analysis (Table 1). The shape of crystallite in estimation of the crystallite size is considered spherical. The amount of carbon z substituting for boron in the crystal lattice of MgB2 (Mg(B1-zCz)2) depends on the lattice parameter a (nm). Considering results from refs. [21-23], the dependence is: z = -21.9 a + 6.76 [20]. Orientation of MgB2 was assessed by using the March Dolase orientation factor r [33, 34 din noi SUST orient1], the degree of orientation  [33, 34 din noi SUST orient1], the orientation angle  [34 din noi SUST orient1 si noi SUST1], and the Lotgering factor LF [35 din noi SUST orient1] (Table 1).   A PPMS-14T (Quantum Design) equipment was used to measure the magnetization curves with temperature m(T) and hysteresis loops m(H) at different temperatures. Samples were cubic, cut from the center of the discs with the size of 1 × 1 × 1 mm3. The critical current density Jc (in Acm−2) was calculated with the Bean formula for a cubic geometry [36 din noi SUST orient1]:    (1)where m is the magnetic moment in emu for the increasing m and decreasing m magnetic field, and l is the side of the cube in cm. The irreversibility field Hirr was determined with the criterion Jc(Hirr) = 102 A/cm2.3. Results and Discussion3.1. Bulk density and structural detailsSamples prepared by SPS have high relative densities, above 94 % (Table 1). The relative density is higher for the partially oriented samples ‘c’ (99 %) and ‘e’ (98%) than for randomly oriented samples ‘b’ (94.7 %) and ‘d’ (97.7 %). The authors of refs. [noi Phys. C primul si din Phys C primul SUST englezii??] found that the influence of relative density on critical current density, when above 90 %, is small. This observation is taken as the background that enables a comparative analysis of the superconducting properties among the randomly and partially oriented samples from this work (see Section 3.2). Samples present also other differences and the reasons are  related to different SPS dwell times at 1150 C, namely 3 min for randomly oriented samples ‘b’ and ‘d’ and 30 min for partially oriented samples ‘c’ and ‘e’, and to the use of PEI during processing of the partially oriented samples ‘c’ and ‘e’. Although partially oriented samples ‘c’ and ‘e’ have higher relative densities as mentioned, they contain a lower weight fraction of MgB2 phase: 70 / 74 wt. % in samples ‘c’ / ’e’ versus 78.9 / 81.4 wt. % in samples ‘b’ / ‘d’. Due to PEI presence during processing, partially oriented samples ‘c’ / ’e’ show higher z-values (0.0192 / 0.146) of carbon substituting into the crystal lattice of MgB2 than for randomly oriented samples ‘b’ / ’d’ (0.0102 / 0.0083). One also observes that z in samples ‘b’ / ‘c’ (0.0102 / 0.0192) added with B4C is higher while the weight fraction of MgB2 is lower (78.9/70 wt.%) than for the corresponding samples ‘d’ / ’e’ (0.0083 / 0.0146 and 81.4 /7 4 wt. %). As expected, B4C reacts with MgB2 [noi Mater Res Bull] and supplies Table 1. March-Dollase orientation factor (r), Lotgering factor (LF), degree of preferred orientation (), orientation angle , lattice parameters of MgB2, amount of carbon (z) in Mg(B1-zCz)2 lattice, crystallite size, residual micro strain, and relative density RSPS and midpoint critical temperature Tc,mid. Sample* r LF[%] / [%]() [] Lattice parameters of MgB2 z Phase content [wt. %] / Crystallite size [nm] Microstrain in MgB2 [%]  RSPS [%] Tc, mid[K]    a [Å] c [Å]  MgB2 MgB4(Mg) MgO    ‘a’ MgB2 raw powder - 0 / - 3.0876 3.5248 0.002 88.0 / 113 4.6(0.3) / 100(91) 7.1 / 31 0.09 - - ‘b’ SPSMBBC randomly oriented - 0 / - 3.0821 3.5277 0.0102 78.9/ 170 13.3 / 72 7.8 / 85 0.175 94.7 37.48 ‘c’ HFSC+ SPS MBBC; Stop 0.796 14 / 13 / (50) 3.0780 3.5246 0.0192 70 / 186 20 / 91 10 / 93 0.15 99 37.42  HFSC + SPS MBBC; Slateral - - - - - 70 / 232 19 / 101 11 / 103 0.12 - 37.02 ‘d’ SPSMBBNrandomly oriented - 0 / - 3.0835 3.5292 0.0083 81.4 / 160 10.9 / 54 7.7 / 116 0.142 97.7 37.98 ‘e’ HFSC+ SPS MBBN; Stop 0.847 9 / 9.4 / (51) 3.0801 3.5247 0.0146 74 / 174 15 / 80 11 / 78 0.14 98 37.88  HFSC + SPS MBBN; Slateral - - - - - 75 / 228 14 / 93 11 / 88 0.11 - 37.85Note: * Notations are: HFSC=high field slip casting; MBBC = MgB2 added with B4C; MBBN = MgB2 added with cubic BN; XRD was performed on Stop= top surface of the disc and on Slateral = surface perpendicular to Stop and parallel to the thickness of the disc.carbon, thus, contributing to enhancement of z. Another source of carbon is the graphite mold used during SPS. The raw powder of MgB2 has the lowest z-value (0.002). In general, a higher z is accompanied by larger values of the micro strain in MgB2. This is valid if we compare randomly oriented samples ‘b’ and ‘d’ or partially oriented samples ‘c’ and ‘e’. Situation changes when samples ‘b’, ‘c’ with B4C and ‘d’, ‘e’ with c-BN are compared:  the dependence between z and micro strain is reversed (Table 1). It is also noteworthy that micro strain presents anisotropy in the partially oriented samples ‘c’ and ‘e’. The micro strain is smaller when XRD is measured on the surface Slateral of the sintered disc (Table 1) than for the surface Stop. This can be understood in the view of differential directional coarsening of MgB2 during SPS, this process being influenced by the MgB2 orientation. The crystallite size of MgB2 in partially oriented samples ‘c’ and ‘e’ when measured on Stop and Slateral show different values, namely for Stop (186, 174 nm) is smaller than for Slateral (232, 228 nm). This tendency is observed also for the phases MgB4 and MgO. The crystallite size of the randomly oriented samples ‘b’ and ‘d’ for phases MgB2 (170 / 160 nm), MgB4 (72 / 54 nm) and MgO (85 / 116 nm) are in general lower than for partially oriented samples ‘c’ and ‘e’ (186 and 232 / 174 and 228 nm for MgB2, 91 and 101 / 80 and 93 nm for MgB4, 93 and 103 / 78 and 88 nm for MgO). An exception is the relatively high value of MgO crystallite size in sample ‘d’. Results suggest that orientation promotes crystallite size enhancement and this is in agreement with our previous findings for partially oriented pristine MgB2 bulk [noi SUST orient 1]. However, the statement needs careful consideration because additives may contribute to different processes including MgB2 orientation and further to crystallite size evolution. Although the influence of the additive on crystallite size is not significant, we note that samples ‘d’ and ‘e’ with an inert c-BN addition show mostly lower crystallite size values (exception is large value for MgO in sample ‘d’) than for samples ‘b’ and ‘c’ with a reactive B4C additive (Table 1). The orientation factors LF and  are higher (March Dollase orientation factor r is smaller) in the sample ‘c’ with B4C ( 13 %) than in sample ‘e’ with inert c-BN ( 9 %) for a similar value of the orientation angle  ( 50 ). The difference may come from the fact that Mg and C form a low temperature Mg-C eutectic (4?? C) [?? Vezi noi Mater Res Bull cu B4C] and this can aid orientation formation during SPS. Noteworthy is also that partially oriented samples with additives from this work present a lower degree of MgB2 orientation than for the pristine sample from ref. [??noi SUST orient1] ( 23 %).This Section indicates on the different influence of the additives when samples are randomly oriented or partially oriented: parameters such as degree of MgB2 orientation, crystallite size, z-carbon, micro strain and phase assembly show changes with different amplitudes. Some tendencies in the partially oriented samples such as carbon behavior and anisotropy of the micro strain require further research.      3.2 Temperature dependence of magnetization and magnetic susceptibility          The temperature dependence of magnetization and of magnetic susceptibility is shown in Fig.1. Zero-field-cooling (ZFC) magnetization was normalized to its value at 35 K, while susceptibility data were normalized to susceptibility of an ideal superconductor id = 1/4 and corrected for demagnetization effects with demagnetization factor N. Measurements were performed in a field of 100 Oe, lower than lower critical field, Hc1 (??? [poate Buzea/Yamashita SUST???]) to avoid the effects of vorticity at low temperatures so that the volume fraction of superconductor can be estimated.  (a) (b)Fig. 1 (a) - Reduced magnetization curves vs. temperature for MBBC and MBBN, oriented and randomly oriented) samples ‘b’-‘e’; (b) - Temperature dependence of the normalized magnetic susceptibility  for samples ‘b’-‘e’ (for partially oriented samples ‘c’ and ‘e’ applied magnetic field H is parallel to H0). Inset shows the temperature dependence of the Meissner fraction fM.The critical temperature of the samples taken as the onset of transition Tc, onset is about 39-39.2 K, i.e. it is considered constant. The shape of the reduced magnetization curves m(T) / m(35 K) versus temperature is different. To compare samples we determined the midpoint critical temperature Tc, mid for m(T) / m(35 K) = 0.5. Values of Tc, mid are gathered in Table 1. Due to a higher z-carbon, in partially oriented samples ‘b’ and ‘d’ the values of Tc, mid are lower and transitions are larger than in randomly oriented ones ‘c’ and ‘e’. Moreover, for sample ‘c’ added with a reactive additive, B4C, the difference in Tc, mid values for the two measurements with applied magnetic field H perpendicular and parallel with Stop is significant, of 0.4 K. One order of magnitude smaller difference (0.03) is encountered for sample ‘e’ (0.03 K) added with an inert additive, c-BN. This result suggests that in the oriented samples, the influence of carbon (especially of the carbon supplied by B4C in sample ‘c’) on Tc, mid is anisotropic. The layered structure of MgB2 with alternating planes of Mg and B provides the background for a different influence of a defect or local strain (e.g. induced by the substitution of B by C) on the electromagnetic properties of the MgB2 crystal in the ab-plane and out-of-plane.    The shielding volume fraction, as obtained from the low temperature data of susceptibility at 5 K (Fig. 1b) is very high in partially oriented samples ‘c’ and ‘e’, of about 87 %. At that temperature, the applied field H is smaller than Hc1 and the sample is expected to be in the Meissner state, i.e., the induced currents would screen the sample from the applied field and sample behaves close to an ideal diamagnetic sample. Therefore, the shielding volume fraction is larger than the real superconducting volume fraction: indeed as addressed in Section 3.1, SPSed samples contain substantial amounts of non-superconducting MgO and MgB4 phases. The ratio between FC (field-cooling) and ZFC susceptibility FC and ZFC (), i.e. the Meissner fraction [A. M. Campbell, F. J. Blunt, J. D. Johnson, and P. A. Freeman, Cryogenics 31, 732 (1991)] at temperatures Tc1 where the lower critical field Hc1 is equal to the measuring field H = 100 Oe, gives information on the strength of the pinning c1 at that temperature [J. R. Clem, Z. Hao, Phys. Rev. B 48 13774 (1993)]. Specifically, fM = f(1-c1/2n), where f < 1 is a dimensionless factor and 1  n  3 depicts the temperature decrease of the critical current density. The Meissner fraction for the two samples partially oriented samples ‘c’ and ‘e’ is small, fM = 0.9 % and fM = 0.79 %, respectively. It indicates that pinning is rather strong in both samples with a slight improvement for the sample ‘e’ with c-BN. The comparison with the randomly oriented samples show a decrease of the Meissner fraction fM and an enhancement of the pinning strength c1:  fM is 1.1 and 0.9 % for samples ‘b’ and ‘c’ added with B4C and it has a more consistent decrease from 2.7 to 0.79 % for samples ‘d’ and ‘e’ added with c-BN.In summary, Section 3.2 indicates on the non-trivial electromagnetic behavior of the samples depending on orientation and additives. For a deeper insight, in the next Section 3.3 the details of critical current density, irreversibility field, and pinning force aspects are addressed.    3.3. Critical current density, irreversibility field, and pinning forceMagnetic critical current densities at 5 and 20 K are presented in Fig. 2 a, b. In partially oriented samples ‘c’ and ‘e’, Jc at high magnetic fields for an applied magnetic field H // H0 is higher than for H  H0 and it is similar or even higher than for the corresponding randomly oriented  (a) (b) (c) (d) (e) (f)Fig. 2 Critical current density curves Jc(0H) at 5 K (a) and 20 K (b); Irreversibility field curves µ0Hirr(T) (c); Irreversibility field µ0Hirr as a function of reduced temperature 1- (T/Tc)2 for partially oriented samples (d) and for randomly oriented samples (inset): lines are fits with eq. (2); Zero-field critical current density curves Jc0(T) (e); (Jc0 x 0Hirr) vs. temperature (g).samples ‘b’ and ‘d’. This result is also reflected by the curves of irreversibility field Hirr with temperature from Fig. 2c. The largest values of Hirr are for sample ‘c’ when H // H0. This result is remarkable since we have seen that the weight fraction of MgB2 is smaller and the crystallite size is larger in the partially oriented samples than in the corresponding randomy oriented ones. A larger crystallite size leads to a lower density of grain boundaries. The grain boundaries are recognized as effective pinning centers in MgB2. A higher density of grain boundaries and better conectivity for less non-superconducting phases are the ingredients for enhancement of Jc and Hirr, but this is the specific situation for the randomly oriented samples with lower Jc and Hirr. Our results enable further enhancement of Jc and Hirr through additives and orientation, and promotes new practical developments.        The irreversibility field (Fig. 2d) roughly obeys the law:,  (2)The exponent  takes close values for partially oriented sample ‘e’ added with BN,  = 1.67  00.08 (H  H0) and  = 1.62  0.05 (H // H0). For sample ‘c’ added with B4C, the difference between the exponents is rather consistent,  =1.76  0.11 (H  H0) and  = 2.13  0.22 (H // H0). Randomly oriented samples, ‘b’ and ‘d’, follow the same temperature dependence (Fig. 2d inset): despite different additives,  -values are not much different, i.e.   = 1.78  0.06 and  = 1.730.0.07, respectively. This paragraph confirms results from the previous one, namely that orientation has a considerable effect on the samples added with B4C. When the amount of carbon in the samples is higher, Hirr is enhanced, but, in general, the zero-field critical current density Jc0 decreases. This tendency can be observed for our samples, although variation among samples ‘b’-‘e’ is within a relatively small range (0.58 – 0.72 MA/cm2 at 5 K). The highest Hirr (as-observed in partially oriented samples ‘c’ and ‘e’ for H // H0) is accompanied by the lowest Jc0 (Fig. 2e). This correlates also with assumed anisotropic influence of the carbon expected from the stronger decrease of Tc, mid for H // H0 than for H  H0, presented in Section 3.2. The relatively more significant variation of Hirr than of Jc0 mostly controls the quality product Jc0µ0Hirr. The lowest values of the product (Fig. 2f) as well as of Hirr (Fig. 2 c) are in the partially oriented samples when H  H0, while for all the other situations the product shows almost similar values. The quality product has no theoretical or practical meaning and it is only used to compare samples from the viewpoint of the balance between the low and high field functional superconducting characteristics of the samples. The dependence of the pinning force, Fp = JcB, normalized by its maximum value, Fp,max with reduced field h = H/Hirr is shown for 20 K in Fig. 3a and for all temperatures in Fig. 1 Supplementary Material. The dependence of Fp,max with temperature is shown in Fig. 3 b. Higher values of Fp,max are for the randomly oriented samples than for partially oriented ones. For the oriented samples ‘c’ and ‘e’ the values of Fp,max when H  H0 and H // H0 are not much different. This situation is not special since the values of Jc are not much different at low and intermediate fields where Fp is maximum.    (a) (b) (c) (d)Fig. 3 (a) - Normalized pinning force fp as a function of reduced magnetic field h at 20 K; (b) - maximum pinning force as a function of temperature; (c), (d) – pinning force parameters h0 and kn as a function of temperature.               Dew-Hughes [Dew-Hughes D 1974 Philos. Mag. 30 293] proposed the following relationship fp = Ahp(1-h)q   (3)and defined h0 = 0.2, p = 0.5, q = 2 for surface (grain boundary) pinning (GBP) and h0=0.33, p = 1, q = 2 for pinning on point defects (PP). The pinning force parameter h0 is h at fp = 1. Considering the percolation aspects, Eisterer [??], introduced the pinning force parameter kn=h0/h1 where h1 = h(fp = 0.5). For PP and GBP it takes the value 0.34 and for GBP 0.47. The dependencies of h0 and kn with temperature are presented in Fig. 3 c and d. In the partially oriented samples ‘c’ and ‘e’ for H // H0, h0 takes unusually low values, around 0.1 at 5 K and 0.18 at 30 K (Fig. 3c). The h0-values for H  H0 are closer to theoretical values and they are similar or lower than for randomly oriented samples. This distribution remains valid for kn, but separation among the curves is larger and kn(‘d’)> kn(‘b’)> kn(‘e’, H  H0)> kn(‘c’, H  H0). When one compares curves of h0(T) and kn(T), the kn(T) curve for sample ‘c’, H  H0 is located at very low kn-values, even below those for sample ‘e’, H // H0. Another observation of interest is that, although both h0 and kn are increasing with temperature, i.e. the share of GBP is stronger at low than at high temperatures, the values of kn are above 0.33 and this suggests that the major pinning mechanism is of PP type. As mentioned, h0 takes low values, between 0.1 and 0.3, and it would correspond to a major GBP mechanism.    Encounted differences in the behavior of h0(T) and kn(T) indicate that the two pinning force parameters are sensitive in a different manner to sample’s specifics. Therefore, kn is not a direct rescaled measure of h0, it is more sensitive than h0, and its physical meaning requires refinement. Presented situation also indicates that different pinning mechanisms are active in our samples and they are depending on the additive and MgB2 orientation.According to eq. (3), the plot of   vs. x = h/(1-h) is supposed to be linear given that p and q exponents are acceptable. However, the plots provide unphysical high exponents for low fields (p ~2, q ~ 10) and more moderate at higher fields (p ~2.5, q ~ 4.5), but also hard to find a correct physical interpretation. Following the analyses of Wordenweber et al. [R Wordenweber, K Heinemann, G V S SastryS and H C Freyhardt 1989 Supercond. Sci. Technol. 2 207] and Eisterer et al. [M. Eisterer, M. Zehetmayer, and H.W.Weber 2003 Phys. Rev. Lett. 90 247002] we searched for a more general relationship:fp = h1/2(1-h)2g(h)       (4)which reduces the question of the functional dependence to that of finding the function g(h) = fph-1/2(1-h)-2.   (5)We assume that GBP is the major pinning mechanism for all our MgB2 samples. The analysis with eq. (5) of our experimental data suggests that g(h) is peaked? (neclar: adica atinge bine maximul lui fp(h), sau? Viorel) and fits well with a distribution function. The right function depends on each sample. In the case of partially oriented samples ‘c’ and ‘e’ (Fig. 1 a-d,  Supplementary Material), which show a shoulder in the fp vs. h dependence, regardless the additive and the orientation of the applied field in the magnetic measurement we needed two Gauss functions. That fact is not valid in the case of the randomly oriented samples ‘b’ and ‘d’ for which g(h) is a single Gauss function (Fig. 1 e. f,  Supplementary Material). The occurrence of the second peak in fp(h) was considered to be primary the consequence of changing connectivity [Koblischka, noi cartea 2020] strongly influenced e.g. by additives distribution in the SPSed superconductor [noi cartea 2020]. For the samples from this work, the presence of the second peak in pinning force only in partially oriented samples ‘c’ and ‘e’ and a better distinguished peak for H // H0 than  for   H  H0 indicate that MgB2 orientation has to be considered, as well. We have presented in Section 3.2 that pinning in the samples is different depending on orientation. The influence of pinning on the second peak of the volume pinning force remains open for further studies.  The first consequence of the proposed functional dependence is that the position of the peak is no more related only to the p and q exponents, which remains the same for all temperatures but also to the parameters of the Gauss function which change with temperature.A second consequence is related to the field dependence of Jc. Instead of the complex dependences previously used and accompanied with a plethora of crossover fields, now, we have a single dependence (Fig. 2 Supplementary Material):   (6)This dependence also explain the field dependence of ln(Jc)/dH vs. H which previously was interpreted as a change in the nature of pining [SUST noi Ref lucrare trecuta]. 4. ConclusionPartially oriented dense discs with a degree of orientation of 13 and 9 % were obtained in added samples with starting compositions (MgB2)0.99(B4C)0.01 and (MgB2)0.99(c-BN)0.01. Samples were fabricated by slip casting under a magnetic field H0 (perpendicular on the surface of the disc) of 12 T and spark plasma sintering. These samples are compared with randomly oriented samples with similar starting compositions obtained by spark plasma sintering.Structural and magnetic characterization indicate that partially oriented samples present anisotropic properties.  Structural details (phase amount, crystallite size, residual micro strain, z-carbon) bring evidence that orientation and addition have a synergistic effect on the evolution of the microstructure. In partially oriented samples, the maximum values of high field critical current density Jc and irreversibility field µ0Hirr are attained for H//H0. These values are higher or similar than for randomly oriented samples. The result enables new possibilities for further MgB2 improvement and application in superconducting devices. Moreover, for H//H0 the critical temperature at midpoint Tc, mid of transition decreases only slightly (up to 0.4 K). This result suggests an anisotropic influence of carbon substituting for boron in MgB2. The volume pinning force Fp, max and Tc, mid are lower in the partially than in the randomly oriented samples. The pinning-force-related parameters h0 and kn depend on the additive and orientation. Their values in the partially oriented samples versus the theoretical ones within Dew-Hughes and percolation models point on a major GBP and PP mechanism, respectively. This contradiction questions the reliability of pinning mechanism assessment based on these parameters. Other different details of their behavior leads to idea that kn is not a direct rescaling of h0 and it needs further studies for the refinement of its physical meaning. It is proposed to scale the normalized volume pinning force vs. reduced magnetic pinning force by involving a Gauss function according to eq. (5) assuming that GBP is the major pinning mechanism. For the randomly oriented samples a single Gauss function works well, while for partially oriented samples (regardless H//H0 or HH0) a double Gauss function was necessary since in these samples a second maximum in Fp occurs. Although the nature of the second peak in the pinning force confirms that it is mainly rooted in connectivity changes influenced by the additive and orientation, our results also point on the pinning contribution. More research is required in this direction.                      (a) (b) (c) (d) (e) (f)Fig. 1 (Supplementary Material) Normalized pinning force fp at different temperatures as a function of reduced magnetic field h for: (a) - sample ‘c’ with B4C, H  H0; (b) - sample ‘c’ with B4C, H // H0; (c) - sample ‘e’ with c-BN, H  H0; (d) - sample ‘e’ with c-BN, H // H0. Continuous lines are fits with Eq. 5 where g(h) is a double Gauss function in (a)-(d) and a simple one in (e) and (f). Observatie: (e) si (f) par identice in afara de curba violet !!!! DE VERIFICAT (Viorel) (a) (b) (b) (d)Fig. 2 (Supplementary Material) Critical current density Jc at different temperatures as a function of applied magnetic field µ0H for: (a) - sample ‘c’ with B4C, H  H0; (b) - sample ‘c’ with B4C, H // H0; (c) - sample ‘e’ with c-BN, H  H0; (d) - sample ‘e’ with c-BN, H // H0; (e) - sample ‘b’ with B4C; (f) - sample ‘d’ with c-BN. Continuous lines are fits with eq. (6) where g(h) is a double Gauss function.  AcknowledgementsAuthors gratefully acknowledge financial support from MCI-UEFISCDI Romania through Core Program PN19-03 (contract no. 21 N/08.02.2019), project POC 37_697 no. 28/01.09.2016 REBMAT, and ERA-M BIOMB 74/2017 (tb pusa toata formula….). Mihai?? References[1] G. Aldica, S. Popa, M. Enculescu, D. Batalu, L. Miu, M. Ferbinteanu, P. Badica. 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