Oxygen-vacancy phase equilibria in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathrm{z}}$ calculated by the cluster variation method

Ordering in the Cu-O basal plane of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathrm{x}}$ is investigated as a function of oxygen content, chemical potential, and temperature. Two-phase diagrams are calculated by means of the cluster variation method applied to asymmetric two-dimensional Ising models with one nearest-neighbor and two second-nearest-neighbor interactions. The interaction parameters selected ensure the stability of the orthorhombic structures near z=7 and for one of the cases also includes a cell-doubling phase at z=6.5. Oxygen pair and point probabilities are studied as a function of temperature under conditions of constant oxygen partial pressure. Comparison of site occupancy and orthorhombic-to-tetragonal second-order transition temperatures with recent experimental data are in excellent agreement.