Monte Carlo studies of oxygen ordering in the ${\mathrm{YBa}}_2$${\mathrm{Cu}}_{3\mathrm{-}\mathrm{x}}$${\mathrm{A}}_{\mathrm{x}}$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ systems (A=Ga,Al)

Monte Carlo simulation with constant oxygen concentration (Kawasaki dynamics) of a lattice-gas model with anisotropic interaction is used to explore the effects of thermal quenching on oxygen ordering in the basal plane of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ and related systems. The oxygen structure factor is calculated for various quenching conditions and for different oxygen concentrations. The growth of the orthorhombic domain is monitored through the q dependence of the oxygen structure factor along the a and b directions. The effect of substituting ${\mathrm{Ga}}^{3+}$ or ${\mathrm{Al}}^{3+}$ ions at Cu(1) chain sites on the oxygen ordering is also discussed within the framework of this model.