Layer-rigidity model and the mechanism for ion-diffusion-controlled kinetics in the bismuth cuprate 2212-to-2223 transformation

Recent transmission electron microscopy (TEM) experiments have shown that the transformation of the Bi cuprate 2212 phase to 2223 phase consists of fast growth of Ca/CuO₂ planes in the Bi-2212 matrix. A theory is proposed which considers the cylindrical void created by the edge dislocation due to the insertion of a Ca/CuO₂ plane to be a channel for fast ion diffusion. A layer-rigidity model is used to estimate the size of the void for Bi-2212/Bi-2223, as well as that for the stacking fault created by heavy-ion irradiation in YBa₂{Cu}₃O₇ (YBCO) compounds. We find the predictions of the model to agree quantitatively with TEM measurements of the structures of ion-irradiated YBCO systems. The calculated void size for Bi-2212/Bi-2223 compounds is consistent with the existence of fast ion diffusion along the ab plane. The experimentally observed time dependence of the volume fraction of Bi-2223 during the transformation is found to be consistent with a one-dimensional diffusion-controlled transformation mechanism, as predicted by our model.