Theory of oxygen diffusion in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ superconducting compound

Oxygen diffusion coefficients in the ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ superconducting compound are calculated by employing the pair approximation of the path probability method. The results show that the diffusion of oxygen in this compound is significantly dependent on the oxygen density and the degree of long-range order. It was found that the oxygen diffusion rate in the tetragonal phase is faster than that in the orthorhombic phase, with activation energies for diffusion of 0.8 and 1.2 eV, respectively, with the rate changing abruptly when the phase transformation takes place. We discuss the relationship between oxygen diffusion and each pair probability in connection with each pair’s interaction energy values. The kinetics of oxygen diffusion obtained from the present model is discussed in the context of experimental values in the literature and with respect to twin boundary diffusion.