The diffusion of O during the annealing of sintered material was investigated by numerically solving the 1-dimensional non-linear diffusion equation for solid and hollow cylinders. The diffusion coefficient was assumed to be a function of both the temperature and of the local concentration of excess O, and was obtained from published experimental data. Three types of cooling scheme were used in the calculations. These were a single-step change in temperature, a linear decrease in temperature followed by a constant temperature, or a temperature decrease involving many steps. The initial and final temperatures were 906C and 450C, respectively. It was found that the shortest annealing time was achieved when the temperature was decreased in many steps, and the longest annealing time occurred when the temperature was changed in a single step. These results agreed with experimental observations. The calculated results indicated that, when the temperature was decreased in many steps, the average concentration of the cylinder increased quite sharply with time until it reached about 90% of the saturation concentration which corresponded to the final temperature. The rate of increase then became small, and continued to decrease. The annealing time could be reduced considerably by using hollow cylinders because O could diffuse into the interior from both the inner and outer surfaces. The results indicated that the reduction in annealing time was much larger than the reduction in total area for current flow. Thus, the annealing time of a hollow cylinder with an inside/outside radius ratio of 1/6 was reduced by more than 50% with respect to that for a solid cylinder, while the reduction in total area that was available for current flow was only 2.8%.

S.Y.Seol, Y.S.Cha: Applied Superconductivity, 1994, 2[1], 7-16