Download 5 Questions of Phase Transformation in Material Processing - Exam 2 | MATL 6300 and more Exams Materials science in PDF only on Docsity!
MATL 5300/6300/6306 Spring 2010
Exam #
Time Allowed 75 min
Name
PLEASE READ THE FOLLOWING BEFORE STARTING
- Please answer all questions in the space provided.
- No credit will be given for irrelevant answers, so please READ THE QUESTIONS with care!
- Credit is given for method as well as for solutions so it is essential that you CLEARLY show how
your answers were derived.
- Put labels and units properly.
c J D x
2
2
c c D t x
2
( , ) exp 4
S x C x t
π Dt Dt
2
( , ) exp 4 4
S x C x t
π Dt Dt
Dt
x C xt Cs erf 2
Dt
x C xt CI Cs CI erf 2
Dt
x erf
C
C xt 2
0
o exp
Q
D D
RT
R = 8.314 J / mol K i =1.987 cal / mol K i
The error function table.
z erf(z) z erf(z) z erf(z) z erf(z)
- Explain using diagrams, words, and equations how you could determine D as a function of
temperature. Be as specific as possible with your answer.
(b) At which places on the bar does the concentration change most as a function of time at
temperature? At which places on the bar does the concentration not change?
(c) What is the final composition of the bar, once homogenization is complete? Prove your answer.
(d) If the temperature were increased from 600 to 700 K, by what factor would the time required to
achieve the same level of homogenization be changed? Give a numerical answer? Note that the
activation energy for diffusion of C in the plain C steel = 60 Kcal/mole.
(b) Plot the nitrogen concentration gradient at a time of 15 hours for a temperature of 600 oC.
(c) For what times at 800 oC will your solutions be valid?
- Grain boundary diffusion is faster than bulk diffusion at temperatures < 0.7 – 0.8 T (^) m (where Tm
is the absolute melting point of the material).
(a) Why is grain boundary (GB) diffusion not faster than bulk diffusion at higher fractions of Tm?
Explain briefly.
(b) Explain the effect of grain size on the diffusion through grain boundary and bulk (use the plot for
the explanation).
