Phase diagram of the superconducting oxide ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathrm{\delta }}$

The superconducting oxide ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathrm{\delta }}$ is found in two structures: a tetragonal structure (T) that is stoichiometric when δ=0, and an orthorhombic (O) structure stoichiometric when δ=1. Assuming that only these phases appear in the phase diagram of the oxide as temperature (t) and δ are varied, it is shown that the phase diagram must have one of two relatively simple forms. The first has a T field at high t and low δ, an O field at lower temperature and high δ, and a T+O two-phase field that separates the two at low t. The second has these features, and also includes an O+O’ two-phase field that results from a miscibility gap in the O phase. A mean-field model is fit to the experimental data, and suggests that the second type of diagram is correct. The calculated phase diagram is presented. The variation of the oxygen partial pressure with δ and t is also discussed.