The thermodynamic equilibrium of the formation process of High-Tc superconducting phase YBa2Cu3O7−x

Analysing the equilibrium state of the formation reaction of the high-T_c superconducting phase 1:2:3 (YBa₂Cu₃O_7−x) on the base of the pressure-temperature-oxygen content (P-T−x) correlation research and using the Van't-Hoff equation, the Gibbs free energy (ΔG_m) of the reaction has been calculated for the first time. It is seen that the absolute value of ΔG_m is not large and of the order of 2.5 kcal · mole⁻¹. This leads to an instability of the 1:2:3 phase. Also, from the calculated values of ΔG_m relative stability regions of the 1:2:3 phase are determined for different values of x. Combinatively analysing the relation lg P = A−B/T (where A – the x-dependent constant, and value of B was determined to be equal to 10518 atm. K) and the value of ΔG_m, we come to the conclusion that the synthesis of YBa₂Cu₃O_{7 − x} when x → 0 must be carried out under high oxygen pressure and low temperature for a lasting time, because the reaction rate is limited by slow diffusion in the solid phase.