Structural transformations in nonstoichiometric ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathrm{\delta }}$

Structural-transformation kinetics in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathrm{\delta }}$ caused by oxygen ordering is considered. The effect of long-range interaction between oxygen atoms, Coulomb repulsion, and strain-induced interaction on oxygen ordering is investigated in terms of crystal-lattice-site diffusion theory. Computer simulations of the diffusion of interacting O atoms give a complicated sequence of atomic-scale and mesoscale structural transformations. It is shown that the transformation path strongly influences the crystallographic structure of the ordered phases. An interrelation between the mesoscale and the atomic structures, which proves to be coupled by the long-range interaction, is found. The following structures are obtained: the primary tweed which transforms into a (110) polytwin structure, the secondary tweed, and the ‘‘glassy’’ state, as well as 2${\mathit{a}}_0$×2${\mathit{a}}_0$ and 2 √2 ${\mathit{a}}_0$×2 √2 ${\mathit{a}}_0$ superstructures. Two structural states, the secondary tweed and the ‘‘glassy’’ state, are shown to be mesoscopic phases—metastable (or stable) phases whose phase identity is mostly determined by their mesoscale rather than atomic-scale structure. The structures and morphologies generated in this computer simulation were reported in many experimental studies.