Question

Rank the magnitudes of the diffusion coefficients from greatest to least for the following systems:(a) Cr in Fe at 600°C; (b) C in Fe at 900°C; (c) Cr in Fe at 900°C. Now justify this ranking. You MUST write a short paragraph to explain your ranking

Answer 1

Answer:

The rank of the magnitude of diffusion coefficients from greatest to least is as follows:

1) "C" in "Fe" at 900°C

2) "Cr" in "Fe" at 900°C

3) "Cr" in "Fe" at 600°C

Explanation:

"C" in "Fe" is an interstitial impurity while "Cr" in "Fe" is a substitutional impurity".

With that being said, interstitial diffusion occurs in "C" in "Fe" systems while substitutional diffusion occurs in "Cr" in "Fe" systems.

Also, Interstitial diffusion is much faster than substitutional diffusion, hence the order we got in the answer.

Also, with increasing temperature, magnitude of diffusion coefficient increases due to the relation;

D =D° Exp (-Qd/RT)

Where;

D° = temperature independent pre-exponential

Qd = the activation energy for diffusion

R = universal gas constant

T = absolute temperature

Answer 2

Answer:

Explanation:

The rank of the magnitude of the diffusion coefficient from greatest to least is as follows:

C in Fe at 900°C > Cr in Fe at 900°C > Cr in Fe at 600°C

Reason

C in Fe is an interstitial impurity while Cr in Fe is a substutional impurity.Therefore interstitial impurity occurs in C in Fe systems,while substutitional diffusion occurs in Cr in Fe system.Interstitial is much faster than substitutional diffusion hence the order

Also with increasing temperature magnitude of diffusion coefficient increases,due to the relation.

     D = D₀exp(-Qd/RT)

Where D₀=Temperature independent per exponential

           Qd= The activation energy for diffusion

             R= Universal gas constant

              T=absolute temperature