Question

Aluminizing is a process were steel is hot-dipped into molten aluminum. The process is often used to protect tailpipes in automotive applications. As the steel is held in the molten aluminum, aluminum will diffuse into the metal. Determine the concentration of Al in the steel 50 μm below the surface of the steel after 10 minutes.

The temperature of the molten aluminum is 1000C and the diffusion coefficient for Al in steel at this temperature is D=7.0x10-13 m2/s. For this calculation assume no other phases form during the process.

Answer 1

Solution.

The diffusion of aluminium into the steel can be described by the time-dependent diffusion equation:

Where C₀ is the initial concnentration of aluminium in the steel sample, Cs is the maximum concentration of Al in the steel (the reference data says it is 82 wt% at this temperature),

The error function erf(y) is given by

,

the values of this integral can be found using a special tables.

For this y, tabulated value of erf(y) = 0.91.