Fick's Second Law$$Nonsteady$-$State Diffusion

$5.$D$3$ The wear resistance of a steel shaft is to be improved by hardening its surface by increasing the nitrogen content within an outer surface layer as a result of nitrogen diffusion into the steel;

the nitrogen is to be supplied from an external nitrogen$-$rich gas at an elevated and constant temperature. The initial nitrogen content of the steel is $0\mathrm{.}002$ wt$\%,$ whereas the surface

concentration is to be maintained at $0\mathrm{.}50wt\%.$ For this treatment to be effective, a nitrogen content of $0\mathrm{.}10wt\%st$ be established at a position $0\mathrm{.}40$ mm below the surface. Specify

appropriate heat treatments in terms of temperature and time for temperatures between $475C$ and $625C.$ The preexponential and activation energy for the diffusion of nitrogen in iron are $3$

${10}^{-7}\frac{m^2}{s}$ and $76,150\frac{J}{m}ol,$ respectively, over this temperature range.