A lattice-gas model for the high temperature oxygen-ordering thermodynamics in YBa2Cu3O6+x is presented, which assumes constant effective pair interactions between oxygen atoms and includes in a simple fashion the effect of the electron spin and charge degrees of freedom. This is done using a commonly utilized picture relating the creation of mobile electron holes and unpaired spins to the insertion of oxygen into the basal plane. The model is solved using the nearest-neighbor square approximation of the cluster-variation method. In addition, preliminary Monte Carlo results using next-nearest-neighbor interactions are presented. The model is compared to experimental results for the thermodynamic response function, kT (partial derivative x/partial derivative mu)T (mu is the chemical potential), the number of monovalent copper atoms, and the fractional site occupancies. The model drastically improves the agreement with measured values of kT (partial derivative x/partial derivative mu)T as CoMPared to bare lattice-gas models. Additionally, the monovalent copper count, in contrast to the standard lattice-gas models, is determined self-consistently and agrees qualitatively with experiment.
Schleger, P., Hardy, W. N., & Casalta, H. (1994). Model for the high-temperature oxygen-ordering thermodynamics in YBa2Cu3O6+x - inclusion of electron spin and charge degrees of freedom. Physical Review B, 49(1), 514-523. https://doi.org/10.1103/PhysRevB.49.514