STABILITY OF 2-ROOT-2X2-ROOT-2 OXYGEN ORDERED SUPERSTRUCTURES IN YBA2CU3O6+X

We have compared the ground-state energy of several observed or propos ed ''2 root 2 x 2 root 2 oxygen ordered superstructures'' [''herringbo ne'' 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 Hamilto nian contains (i) the Madelung energy, (ii) a term linear in the diffe rence 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 determi ned, 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 reg ularly spaced O vacancies added to the x=1 structure is more stable th an the corresponding CS for the same x. We find that the detailed posi tions of the atoms in the structure and long-range Coulomb interaction s are crucial for the electronic structure, the mechanism of charge tr ansfer, the stability of the different phases, and the possibility of phase separation.