Using the table 5.2 in text, a) Calculate the dffusion coefficient D for copper

Question

Using the table 5.2 in text,

a) Calculate the dffusion coefficient D for copper (Cu) in aluminum (Al) at 500 degrees C.

b) What time will be required at 600 degrees C to produce the same diffusion result ( in terms of concentration at a specific point) as for 10 hrs at 500 degrees C.

The table reads:

Diff. species___ Host Metal___ Do____ Qd(kJ/mol)___ Qd(eV/atom)____ T(C)___ D(m2/s)

Cu____________Al____ 6.5*10-5 ____136___________ 1.41_______ 500____ 4.1*10-14

Please show equation set-up and all work.

I'm pretty sure I need to equate to equations to one another, but I'm a little confused on that. I believe the equations looks like:

D = Do exp(-Qd/RT)  and [(Cx-Co)/(Cs-Co)] = 1 - erf [ x / (2*sqrt ( D*t))]

THANKS!!

Explanation / Answer

Solution:

Let us go to the basics first.

We are calculating part (b):
From Fick’s second law, we know that:

Dt = constant

=>D600t600 = D500t500

=>t600 = D500t500 / D600

=>t600 = (4.8x10-14 m2s-1)*(10 hours) / (5.3x10-13 m2s-1)

[The diffusion coefficients for copper in aluminum at 500 and 600°C are 4.8x10-14 and 5.3x10-13 m2s-1, respectively.]

=>t600 = 0.90 hour = 54 minutes (Answer )

Thanks!!!

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.