Calculate Nitrogen from a gaseous phase is to be diffused into pure iron at 700oC. Ifthe surface concentration is maintained at 0.1 wt% N, what will be theconcentration 1 mm from the surface after 10h? The diffusion coefficient fornitrogen in iron at 700oC is 2.5×10-11 m2
Question
Calculate Nitrogen from a gaseous phase is to be diffused into pure iron at 700oC. Ifthe surface concentration is maintained at 0.1 wt% N, what will be theconcentration 1 mm from the surface after 10h? The diffusion coefficient fornitrogen in iron at 700oC is 2.5×10-11 m2
Solution
To solve this problem, we can use Fick's second law of diffusion, which is used to determine the concentration of a diffusing species at a particular point in space at a particular time. The equation is:
C = C0 + (Cs - C0) * [ 1 - erf((x / (2 * sqrt(D * t))))]
Where: C is the concentration at a particular time and at a particular position. C0 is the initial concentration. Cs is the surface concentration. x is the position. D is the diffusion coefficient. t is the time. erf is the error function.
Given in the problem: Cs (surface concentration) = 0.1 wt% N = 0.001 C0 (initial concentration) = 0 (since it's pure iron, there's no nitrogen initially) D (diffusion coefficient) = 2.5×10^-11 m^2/s x (position) = 1 mm = 1 x 10^-3 m t (time) = 10 hours = 10 * 60 * 60 seconds = 36000 s
Substituting these values into the equation:
C = 0 + (0.001 - 0) * [ 1 - erf((1 x 10^-3) / (2 * sqrt(2.5×10^-11 * 36000)))] C = 0.001 * [ 1 - erf(0.00001290994)] C = 0.001 * [ 1 - (-0.00001290994)] C = 0.001 * 1.00001290994 C = 0.00000100001290994
So, the concentration of Nitrogen 1 mm from the surface after 10 hours will be approximately 0.000001 or 0.0001 wt% N.
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