PHASE-SEPARATION AND DEVILS STAIRCASE IN MODELS FOR O ORDERING IN RBA2CU3O6+X

When the Gibbs free energy G of a solid solution depends on a free variable eta, which is determined minimizing G, a negative contribution to the second derivative of G with respect to the compositional parameter arises. Under certain circumstances, this term is the dominant one and phase separation is favored. Here we consider the specific case of different two-dimensional lattice-gas models of O ordering in RBa2Cu3O6+x (R=Y, rare earths) in the regime of compositions and parameters for which the O atoms are ordered in infinite Cu-O chains at temperature T=0. When a phenomenological term that takes into account the dependence of the lattice parameter c on the O content x is added to G, phase separation with two broad two-phase fields takes place at T less than or similar to 400 K in the asymmetric next-nearest neighbor Ising (ASYNNNI) model. If instead any two 0 ions interact via a screened Coulomb repulsion, and c is kept fixed, we obtain further evidence of the existence of a complete devil's staircase at T=0. However, when c is relaxed, for any finite screening length only a finite number of phases are stable at T=0 and phase separation also occurs at low enough temperatures.