DIFFUSION AND COOLING RATE DURING ANNEALING OF SINTERED BULK YBA2CU3O7-X

Oxygen diffusion during annealing of sintered YBa2Cu3O7-x is investiga ted by numerically solving the one-dimensional, nonlinear, diffusion e quation for solid and hollow cylinders. The diffusion coefficient is a ssumed 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 numeric al calculations: (1) a single-step change in temperature, (2) a linear decrease in temperature followed by a constant temperature, and (3) a temperature decrease in many steps. The initial and final temperature s are 900 degrees C and 450 degrees C; respectively. The shortest anne aling time is achieved where the temperature is decreased in many step s, and the longest annealing time occurs when the temperature is chang ed in a single step. These results agree with experimental observation s. The calculated results indicate that where the temperature is decre ased in many steps, the average concentration of the cylinder increase s relatively sharply with time until it reaches approximately 90% of t he saturation concentration corresponding to the final temperature. Fr om then on, the rate of increase becomes small and continues to decrea se. Annealing time can be reduced considerably by using hollow cylinde rs because oxygen can diffuse into the interior from both interfaces a t the inner and outer radii. The results indicate that the reduction i n annealing time is much larger than the reduction in total area for c urrent flow. For example, annealing time of a hollow cylinder with r(i )/r(o), = 1/6 would be reduced by more than 50% relative to that of a solid cylinder, while the reduction in total area available for curren t flow is only 2.8%.