OXYGEN SUPERSTRUCTURES IN SEMICONDUCTING RBA2CU3O6+X

We study the ground state and weakly excited oxygen superstructures of RBA2Cu3O6+x, where R = Y or a rare earth, using a model lattice gas Hamiltonian introduced earlier by the authors. This model assumes that any two O ions of the CuOx planes repel each other with a screened Coulomb interaction, but the repulsion between second-neighbour O ions with a Cu ion in between is reduced by a factor f. The value of f was calculated using the extended Hubbard Hamiltonian in the strong-coupling limit. For large screening length-lambda, R = Y and x = 3/8 the predictions of the model are in excellent agreement with recent neutron measurements. Assuming that lambda-decreases strongly in the metallic phase, all previously observed diffraction patterns for R = Y can also be explained (x = 1/8, 1/2, 4/7, 3/5, 5/8, 2/3, 3/4 and 7/8). We conclude that Cu-O chains can be observed almost exclusively in the metallic phase and predict superstructures that should be observed in semiconducting materials, in particular when x greater-than-or-equal-to 1/2 and the ionic radius of R3+ is larger than that of Y3+.