At 700 C, an YBa 2 Cu 3 O 7 sphere of 2 cm radius is abruptly

At 700 °C, an YBa₂Cu₃O_7−δ sphere of 2 cm radius is abruptly exposed to 1 bar O₂ gas. Assuming DO = 10⁻⁵ cm²/s and diffusion as the rate-controlling process, calculate how long it will take before 90% of the total oxidation change occurs 1 mm below the surface. Under these conditions, the sphere center will oxidize by less than 1%, so that the sphere can be approximated as an infinite half-space.