Abstract Oxygen diffusion during annealing of sintered YBa 2 Cu 3 O 7−x is investigated by numerically solving the one-dimensional, nonlinear, diffusion equation for solid and hollow cylinders. The diffusion coefficient is assumed to be a function of both temperature and local concentration of excess oxygen and is obtained from experimental data reported in the literature. Three types of cooling schemes are employed in the numerical calculations: 1. (1) a single-step change in temperature, 2. (2) a linear decrease in temperature followed by a constant temperature, and 3. (3) a temperature decrease in many steps. The initial and final temperatures are 906°C and 450°C; respectively. The shortest annealing time is achieved where the temperature is decreased in many steps, and the longest annealing time occurs when the temperature is changed in a single step. These results agree with experimental observations. The calculated results indicate that where the temperature is decreased in many steps, the average concentration of the cylinder increases relatively sharply with time until it reaches approximately 90% of the saturation concentration corresponding to the final temperature. From then on, the rate of increase becomes small and continues to decrease. Annealing time can be reduced considerably by using hollow cylinders because oxygen can diffuse into the interior from both interfaces at the inner and outer radii. The results indicate that the reduction in annealing time is much larger than the reduction in total area for current flow. For example, annealing time of a hollow cylinder with r i r o = r1 6 would be reduced by more than 50% relative to that of a solid cylinder, while the reduction in total area available for current flow is only 2.8%.
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