Answer to Question #260475 in Material Science Engineering for IST

Question #260475

A diffusion couple is made from nickel and iron. After 30 hours of heat treatment at 1400 K, 

the concentration of nickel is 3.2 wt % at a distance of 1.5 mm from interface. If an identical 

diffusion couple is heated at 1200 K for 30 hours, at what depth from the interface will the 

concentration of nickel be 3.2 wt %? The pre-exponential factor (Do) and activation energy for 

diffusion is 1.8 x 10-5 m2

/s and 152 kJ/mol respectively, and the surface concentration of nickel

is 100 wt%. (Note that this is a non-steady state diffusion process).


1
Expert's answer
2022-02-08T08:52:02-0500

We will use the following solution for Fick's second law for a diffusion couple for this problem:

Cx = C2 + (C1 - C2)/2 x [1 - erf(x/2√Dt)]

C1 is impurity at x < 0 and C2 is impurity content for x > 0. Let us consider Ni as impurity and it is kept at x < 0. Then C1 = 100 wt % of Ni, C2 = 0.

When concentration is constant

C2 + (C1 - C2)/2 x [1 - erf(x1/2√D1t1)] - C2 + (C1 - C2)/2 x [1 - erf(x2/2√D2t2)]

x1/√D1t1 = x2/√D2t2

x1 = 1.5 mm, x2 = x mm, t1 = 30 h, t2 = 30 h.

2.25 / D1 = x2 / D2

D2 = x2D1/2.25

D0 x exp(-Qd/RT2) = x2D0/2.25 x exp(-Qd/RT1)

-Qd/RT2 = ln(x2) - ln 2.25 - Qd/RT1

- 152 000 J/mol / (8.31 J/mol K х 1200 K) =

ln(x2) - 0.81 - 152 000 J/mol / (8.31 J/mol K х 1400 K)

x = 2.10 mm


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS