homework7solution - Solution to Homework #7 Problem 1. a....

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Solution to Homework #7 Problem 1. a. The effective charge Z* for carbon in α -Fe is -12. An electric field of 0.01V/mm is maintained in a 1mm long sample of an Fe-C alloy at a temperature of 700 o C. What will be the concentration ratio between the two ends at the steady state? b. If the initial atom fraction of carbon in the alloy was 0.0005, what fraction of the length of the sample is at a concentration lower than 0.0005 at steady state, if no carbide forms? Solution a. The mass flux in a electrical field is given by = E T k eZ C dx dC D J B 1 1 1 1 1 where C 1 is the carbon concentration. At steady state, 0 1 = J , hence, E T k eZ C dx dC B 1 1 1 = Integrate the above differential equation, () ( ) = x B x C C dx T k E eZ C dC 0 1 0 1 1 1 1 we have ln C 1 x ( ) C 1 0 () = eZ 1 E k B T x or ( ) () = x T k E eZ C x C B 1 1 1 exp 0 Therefore, () () ( ) 24 . 0 1 973 10 38 . 1 01 . 0 12 10 6 . 1 exp exp 0 23 16
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This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Pennsylvania State University, University Park.

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homework7solution - Solution to Homework #7 Problem 1. a....

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