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Material Type: Exam; Professor: Kim; Class: PHASE TRANSFORMATIONS IN MATERIAL PROCESSING; Subject: Materials Engineering; University: Auburn University - Main Campus; Term: Spring 2010;
Typology: Exams
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MATL 5300/6300/6306 Spring 2010
Exam #
Time Allowed 75 min
Name
PLEASE READ THE FOLLOWING BEFORE STARTING
your answers were derived.
c J D x
2
2
c c D t x
2
( , ) exp 4
S x C x t
2
( , ) exp 4 4
S x C x t
Dt
x C xt Cs erf 2
Dt
x C xt CI Cs CI erf 2
Dt
x erf
C xt 2
0
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)
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?
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).