Determination of the Copper Valency and the Oxygen Deficiency in the High Tc Superconductor, $YBa_2Cu_3O_{7-\delta}$

The ratio of trivalent to divalent copper has been determined by the redox titration for two superconducting phases of $YBa_2Cu^{3+}_{2x}Cu^{2+}_{3-2x}O_{6.5+x}$ with the onset temp. of 60K (x = 0.23 ${\pm}$ 0.01) and 90K (x = 0.35 ${\pm}$ 0.02), and for the insulating one (x ${\cong}$ 0) which was kept in an ambient atmosphere for 72 hrs. It is found that $T_c$, and the ratio of $Cu^{3+}/Cu^{2+}$ depend strongly on the annealing temperature and time. A typical orthorhombic phase can easily be obtained by a slow cooling or stepwise cooling at $PO_2$ = 1 atm, and shows a high Tc (ca. 90K) superconductivity.