Ground state of the atomic structure of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$

We study the ordering of O atoms in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ using a two-dimensional Ising model. We assume a screened Coulomb repulsion between any two O ions of the ${\mathrm{CuO}}_{\mathit{x}}$ planes, but the interaction between second-neighbor O ions with a Cu ion in between is reduced by a factor f due to charge-transfer effects. We construct the symmetry-independent atomic configurations, which enable us to compare the energy of a large number of structures. We obtain a rich x-f phase diagram that for screening lengths larger than ∼1 Å and low values of f contains structures compatible with all the diffraction patterns so far observed. The ground state consists of structures composed of linear CuO chains for f<0, or x near 0.5 and f<1, while for f=1 simple lattices of nearly hexagonal symmetry of O ions or vacancies added to the x=1 structure dominate.