The relationship between the porosity and elastic moduli of the Bi-Pb-2212 high-T_c superconductor

A series of Bi-Pb-2212 high-T_c superconductors, having different porosities has been prepared by the solid-state reaction method. After the usual characterization of the samples by XRD, AC susceptibility, SEM, bulk-density and porosity studies, longitudinal (V_l) and shear (V_s) wave velocity measurements have also been undertaken by the pulse-transmission technique. Using the experimental values of V_l and V_s, the Young's moduli (E) of all the samples have been calculated and are later corrected to zero porosity by employing a number of theoretical equations. The corrected moduli are compared with the literature value, which itself has been arrived at by averaging the available single-crystalline stiffness constants. It is concluded from the results that among all the formulae, Mackenzie's equation and that proposed by the authors of the present investigation are in closest agreement with the literature value.