Aluminum-copper alloy(96 atom% Al; 4 atom% Cu) is solution-annealed at 550C and then aged at 450C. At 450C, a CuAl_2 precipitate (67 atom% Al; 33 atom% Cu) is in equilibrium with an Al-Cu solid solution (99 atom%Al ; 1 atom% Cu). The diffusivity of Cu in Al is 1E-14 m^2/sec at 450C. Adopt Zener's model for diffusion-controlled growth of plate- like precipitates.
a) calculate the growth rate dX/dt (m/sec) at t =20,000 sec.
b) calcuate the time required to grow the precipitate half-thickness from X=0 to x=1E-6m.