### Abstract:

An important fundamental problem in the understanding of the high-Tc superconducting systems is the determination of their equilibrium magnetization behaviour, in particular their constitutive Brev(H) orMrev(H) behavior. Single crystal specimens of these materials are typically small (order of micron/millimeter), and are generally in the form of platelets. Their superconductivity properties are, moreover, highly anisotropic. The magnetization [M(H0)] curves in these systems also manifest a hysteresis due to vortex pinning, and, at fields below the lower critical field Hc1, due to a “geometry” effect, which results from a non-uniform internal field distribution in the platelet specimen geometry in a perpendicular applied magnetic field H0. In the present work a brief review of the field is given and a treatment (due to Doyle and Labusch) of the problem is described in some detail, and is used in the analysis of magnetization data [M(H0)] on single-crystal platelet specimens of the YBCO and BSCCO high-Tc superconducting systems. The treatment, which is based on a rigorous theoretical analysis of a quasi-static arbitrary distribution of vortices in a specimen of arbitrary shape (Labusch and Doyle ), predicts the quasi-static magnetization behavior M(H) of the specimen, and allows for the inclusion of explicit relations for the equilibrium “constitutive” Brev(H, T), and for the bulk vortex pinning force density Pv(B). An analytical formula for Brev(H, T) in terms of the fundamental characteristic properties ?ij(T) (the anisotropic Ginsburg -Landau parameter) and the critical field Hc(T) (or the lower critical field Hc1(T)) is obtained from an accurate model fit to a numerical solution of the non-linear Ginsburg-Landau equation (Labusch and Doyle ). For the determination of ? and Hc c1, (i.e. the G-L parameter and the lower critical field along the crystalline c- axis of platelet specimens) from M(H0, T) experimental isotherms (where H0 is the magnetic field applied along the c-axis -the thin dimension of the platelet specimens), a computer algorithm, which incorporates the above treatments, was used. In order to obtain a fit between theoretical model results (of the numerical algorithm for equilibrium behavior) and the experimental M(H0, T) data, experimentally obtained hysteresis curves were averaged by taking the mean values of M(H0) for H0 increasing and decreasing over the entire M(H0) loop. This data was then normalized by Hc1(T) for both M and H0, with Hc1(T) and ?(T) being used as fitting parameters.