A dense, pure polycrystalline MgO has an average grain size of 1 microns, and the grain growth follows normal, parabolic kinetics. Estimate what the average grain size will be after 5 h annealing at 1700 C, given that the grain boundary diffusion coefficient is Dgb = 10^-8 cm2 /sec, the grain boundary width gb = 0.5 nm, and the grain boundary energy gb = 0.5 J/m2 . If some SiO2 is present, leading to the formation of a continuous, liquid film with a thickness of 50 nm at the grain boundaries, estimate the change in the boundary mobility if the diffusion coefficient through the liquid DL is

a. Equal to Dgb

b. Equal to 100Dgb