For some applications, it is necessary to harden the surface of a steel (or iron-carbon alloy) above that of its interior. One way this may be accomplished is by increasing the surface concentration of carbbon in a process termed carburizing; the steel piece is exposed, at an elevated teperature, to an atmosphere rich in a hydrocarbon gas, such as methane (CH4).
Consider one such alloy that initially has a uniform carbon concentration of 0.25 wt% and is to be treated at 950ºC (1750ºF). If the concentration of carbon at the surface is suddenly brought to and maintained at 1.20 wt%, how long will it take to achieve a carbon content of 0.80 wt% at a position 0.5 mm below the surface? The diffusion coefficient for carbon in iron at this temperatiure is 1.6 x 10E-11 m^2 / sec; assume that the steel piece is semi-infinite.
Refernce Callister, Jr., William D., Materials Science and Engineering: An Introduction, Third Edition, John Wiley & Sons, New York, NY, 1994.