Stability of 2√2x2√2 oxygen ordered superstructures in YBa2Cu3O6+x

We have compared the ground-state energy of several observed or proposed "2 root 2 x 2 root 2 oxygen ordered superstructures" ["herringbone" structures (HS's)], with those of "chain superstructures" (CS's) (in which the O atoms of the basal plane are ordered in chains), for different compositions x in YBa2Cu3O6 divided by x. The model Hamiltonian contains (i) the Madelung energy, (ii) a term linear in the difference between Cu and O hole occupancies which controls charge transfer, and (iii) covalency effects based on known results for t-J models in one and two dimensions. The optimum distribution of charge is determined, minimizing the total energy, and depends on two parameters which are determined from known results for x=1 and x=0.5. We obtain that on the O lean side, only CS's are stable, while for x=7/8, a HS with regularly spaced O vacancies added to the x=1 structure is more stable than the corresponding CS for the same x. We find that the detailed positions of the atoms in the structure and long-range Coulomb interactions are crucial for the electronic structure, the mechanism of charge transfer, the stability of the different phases, and the possibility of phase separation.