Compute diffusion coefficients for the interdiffusion of carbon in both (a) α-iron (BCC) and (b) γ-iron (FCC) at 1000˚C. Assume that D0 for the interdiffusion of carbon in α-iron and in γ-iron are 1.1 × 10-6 and 2.3 × 10-5 m2/s, respectively, and that Qd are 80 and 148 kJ/mol, respectively.

Explanation:

According to Ficks first law, the relation between diffusion flux and diffusion coefficient is as follows.

             J =

where, D = function of temperature

         D =

where,   = pre-exponential independent of temperature

(a)  Substituting the given values into the above formula, we will calculate the value of D as follows.

                   D =

                      =

                      =

                      =

                     =

Therefore, diffusion coefficient for the inter-diffusion of carbon in -iron is .

(b)   For -iron we will calculate the value of D as follows.

                D =

                      =  

                      =

                      =

                      =

Therefore, diffusion coefficient for the inter-diffusion of carbon in -iron is .

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