Thermodynamics of oxygen ordering in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{\mathrm{z}}$

The ordering in the Cu-O basal plane of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathrm{z}}$ is investigated as a function of oxygen content and temperature. A phase diagram is calculated by application of the cluster variation method to an asymmetric two-dimensional Ising model. The interaction parameters selected guarantee the stability of the experimentally observed double-cell structure around z=6.5. The transition temperatures at various oxygen partial pressures are in good agreement with experiment. The pair probabilities along the Cu-O chains show a plateau with varying oxygen concentration, not unlike the dependence of ${\mathrm{T}}_{\mathrm{c}}$ on oxygen content.