Use the diffusion data in the table below for atoms in iron to answer the questions that follow. Assume metastable equilibrium conditions and trace amounts of C in Fe. The gas constant in SI units is 8.314 J (mol K).
|
Diffusion |
Diffusion |
||
|
Couple |
Mechanism |
Q (J/mol) |
D0 (m2/s) |
|
C in FCC iron |
Interstitial |
1.38 × 105 |
2.3 × 10-5 |
|
C in BCC iron |
Interstitial |
8.74 × 104 |
1.1 × 10-6 |
|
Fe in FCC iron |
Vacancy |
2.79 × 105 |
6.5 × 10-5 |
|
Fe in BCC iron |
Vacancy |
2.46 × 105 |
4.1 × 10-4 |
(a) Plot the diffusion coefficient as a function of inverse temperature (1/T) showing all four diffusion couples in the table.
(b) Recall the temperatures for phase transitions in iron, and for each case, indicate on the graph the temperature range over which the diffusion data is valid.
(c) Why is the activation energy for Fe diffusion higher than that for C diffusion in iron?
(d) Why is the activation energy for diffusion higher in FCC iron when compared to BCC iron?
(e) Does C diffuse faster in FCC Fe than in BCC Fe? Support your answer with a numerical calculation and state any assumptions made.
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