How Does Atom Diffusion Vary in Different Iron Phases?

[ser_hm2]

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.

 

[Navin A S]

a) The diffusion coefficient as a function of inverse temperature (1/T) is plotted below.b) The temperatures for phase transitions in iron are:FCC to BCC at 910°C, and BCC to liquid at 1495°C. The diffusion data is valid for temperatures between 910°C and 1495°C. c) The activation energy for Fe diffusion is higher than that for C diffusion in iron because Fe atoms are larger than C atoms and thus require more energy to move through the lattice.d) The activation energy for diffusion is higher in FCC iron when compared to BCC iron because the lattice structure of FCC iron is more tightly packed than that of BCC iron, which makes it more difficult for an atom to move through the lattice. e) C does diffuse faster in FCC Fe than in BCC Fe. The diffusion coefficient for C in FCC iron (D0 = 2.3*10-5 m2s-1) is higher than that of C in BCC iron (D0 = 1.1*10-6 m2s-1). Assuming that the activation energies for C diffusion are the same in both FCC and BCC iron, the ratio of the diffusion coefficients can be calculated using the Arrhenius equation: D0_FCC/D0_BCC = exp((Q_BCC - Q_FCC)/(8.314*T)) where T is the absolute temperature. At 1000K, this ratio is approximately 20, meaning that C diffuses 20 times faster in FCC iron than in BCC iron.