Oxygen Ordering in YBa₂Cu₃O_6+x

The orthorhombic and tetragonal phase relation, i.e. the order-disorder phase transformation in YBa₂Cu₃O_6+x, has been studied by employing statistical thermodynamics, and the equilibrium value of order parameter -1≦s≦1 has been determined as a function of the temperature and oxygen concentration. In the above-mentioned treatment, plus and minus signs of s in the ordered state (|s|≠0) are found to describe the degree of order in the twin related crystals. The calculated properties are compared with the experimental data, i.e. the temperature dependence of oxygen occupancy at a constant oxygen pressure and the concentration dependence of axial lengths, a and b, at room temperature. The agreement is excellent for both cases when the axial lengths at room temperature are measured for the samples with oxygen removed or doped at low temperatures. The statistical thermodynamical expression for further ordering has also been derived.