The from percolation theory considerationstakes values of 0.47

The magnetic hysteresis loops m(B) at different temperatures were registered with aVibrating Sample Magnetometer (VSM-9T, Cryogenic) on the MgB2 core. Samples wereparallelipipeds cut from the center of the core tapes and had dimensions L x l x g of about 1.6mm x 1.4 mm x 0.24 mm. The critical current density at different temperatures, Jc, wasdetermined from the m(B) experimental loops with Bean formula for a plate-like geometry19:Jc = 20?|m?-m?|/(V?l?(1-(l/(3?L)))) (1)where m is magnetic moment in emu on ascending and descending magnetic field, V – thesample volume in cm3, and L, l are in cm. Prior to Jc estimation, corrections of the magnetichysteresis loops were undertaken to eliminate the magnetic contribution of the impurities andof the holder. Self-field Jc0 (in A/cm2) was determined for a modified Bean relation, a platelikegeometry 20, and considering the descending branch of the hysteresis loop 21:Jc = 60??m? ?/(V?l) (2)This approach is useful to avoid the complications with the flux jumps (that occur in the lowtemperature m(B) loops) and further estimation of |m?-m?| in the classic Bean model. Usingthe classic Bean model, the pinning force Fp was extracted and reduced pinning force fp= Fp /Fpmax, was plotted as a function of reduced magnetic field h=H/Hirr 22. The irreversibityfield Hirr was determined from the m(B) loops for a criterion of 100 A/cm2. Experimental datawere fitted with universal scaling function fp = Ahp(1-h)q 23. Pinning-force-relatedparameters p, q, and h0 (h0=h(Fpmax)) provide information on the pinning mechanism. For apoint pinning (PP) mechanism p, q and h0 are taking values 1, 2 and 0.33, while for the grainboundary pinning (GBP) the values are 0.5, 2 and 0.2 24. The parameter kn = Hpeak / Hn,where Hpeak = H(Fpmax) and Hn = H(1/2 Fpmax) 25 from percolation theory considerationstakes values of 0.47 and 0.34 for PP and GBP, respectively. Curves of m(T) under zero-fieldcoolingconditions were measured with a magnetic field of 100 Oe applied parallel to thethickness of the MgB2 core.The resistivity as a function of temperature under an applied magnetic field ?0H = 0 –14 T was investigated on the peeled tape’s MgB2 core using the four-probes method (PPMSQuantumDesign, US). The measuring current was 2 mA and it was applied in the (L x l)-plane, along the L-direction, while ?0H was parallel to g. Electrical contacts were made withAg-paste. The irreversibility Hirrelectric and upper critical Hc2electric fields were determined for acriterion of 10 % and 90 % of the superconducting transition in the resistivity curve