Twin and tweed microstructures in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ doped by trivalent cations

Computer-simulation techniques and TEM analysis were employed to study the dependence of the twin and tweed microstructures in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$ ${\mathrm{M}}_{\mathit{x}}$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ on doping by trivalent atoms (like Fe, Co, or Al). Since the trivalent atoms substituting the bivalent Cu(I) atoms have a greater number of the nearest-neighbor oxygen atoms, it was suggested that doping can be described by the M-O nearest-neighbor attractive interaction. This interaction generates a local oxygen disorder which plays an important role in the formation of the tweed structure. The M-O interaction and the long-range O-O interaction (screened Coulomb and strain induced) were taken into account to simulate the oxygen ordering kinetics. The simulation is based on equations describing the microscopic diffusion of oxygen atoms. The obtained simulated microstructures are in qualitative and even quantitative agreement with electron microscopic observations for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_{3\mathrm{-}\mathit{x}}$ ${\mathrm{Fe}}_{\mathit{x}}$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and with previous electron microscopic data. Both the computer simulations and the TEM results have shown that the usual twin structure, formed through coarsening and refining of the transient tweed structure, is produced at small doping (x≤∼0.08). At larger x(∼0.08<x<∼0.2–0.3), the dopant atoms prevent coarsening and a metastable (or stable) mesoscopic tweed pattern appears. Although the crystal lattice is locally distorted by ultrafine orthorhombic domains forming the tweed pattern, the average crystal lattice determining the diffraction spot pattern is tetragonal. At higher x, the ultrafine orthorhombic domains producing the tweed structure disappear and a disordered tetragonal phase is formed. It is found that doping does not affect the microstructure if the long-range model for the M-O interactions is assumed.