Fe $0\mathrm{.}15$ wt$\%$ C is carburized at an elevated temperature and in an atmosphere that gives a surface C content of $1\mathrm{.}15$ wt$\%.$ You are requested to design a $3-$day treatment process that will produce steel with carbon concentration of $0\mathrm{.}30$ wt$\%$ at a position of $30\mathrm{.}0$ m from the surface. Answer the following:$($i$)$ Justify whether the process will produce BCC or FCC phase.$($ii$)$ Determine the diffusion coefficient of carbon during the process.