Chapter 5, Problem 5.62P

Interpretation Introduction

Interpretation:

If iron is FCC and 1.10% C is present at the surface, the temperature required to obtain 0.50% C at a distance of 0.5mm beneath the surface of a 0.20% C steel in 2 hours needs to be determined.

Concept introduction:

Fick's second law equation is given by the following relation:

$\frac{Cs-Cx}{Cs-Co}=erf(\frac{x}{2\sqrt{Dt}})$

Here,

D = diffusion coefficient

Cs = constant concentration for the material surface of diffusion atoms.

Co = initial concentration of diffusion on

Cx = diffusing concentration atom at location x

T = time

Also, diffusion coefficient for carbon in FCC by Arrhenius type equation relation is as follows:

$D_{acc}=D_o\exp (\frac{-Q}{RT})$

Here,

Dacc = diffusion coefficient

Do = constant

Q = activation energy

R = Gas constant

T = absolute temperature