Inhomogeneous distribution of the pinning force in superconductor results in a magnetization asymmetry. A model considering the field distribution in superconductor was developed and symmetric and asymmetric magnetization loops of porous and textured
Bi_{1.8}Pb_{0.3}Sr_{1.9}Ca_{2}Cu_{3}O_{x} were fitted. It is found that the thermal equilibrium magnetization realizes in crystals smaller than some size depending on temperature and magnetic field.
The dependence of magnetization on magnetic field M(H) was measured for textured BSCCO samples for H || c, H || ab at different temperatures. Inclusion of the pinning parameter in the Valkov-Khrustalev model [V.V. Valkov, B.P. Khrustalev, JETP 80 (19
95) 680] allowed to describe successfully the asymmetric M(H) dependencies. The temperature and magnetic field dependencies of critical current and pinning parameter for H || c and H || ab were estimated.
The intragrain pinning in high-$T_c$ superconductor compounds Y$_{1-x}$RE$_{x}$Ba$_{2}$Cu$_{3}$O$_{7-delta}$ with low concentration of RE (La, Ce, Pr) was investigated. Magnetic and transport measurements reveal that the pinning is maximal for the co
ncentration of heterovalent RE such that the average distance between the impurity ions in the plane of rare-earth elements close to the diameter of Abrikosov vortices in YBCO.
