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Solutionset04_2007

# Solutionset04_2007 - Seoul National University The...

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Seoul National University The University of Tokyo Kinetic Processes in Materials Solution Set #04 Nov., 08, 2007 Prof. Han-Ill Yoo 1. Velocity of the markers follows below equation. x / N ) D D ( v A B A 0 x / N and , 0 ) D D ( A B A . Therefore v is negative sign, and the markers are shifted to the higher A concentration side. Initially x / N A is large at the weld interface, and zero at the markers away from the discontinuity in composition. Thus, the markers at the weld interface will start moving immediately faster, while the other set will move only as the gradient, x / N A , at that location rises. 2. If we assume D=const, when it is x const. Dt , then c is x c c const. Dt . And so x A t (A: constant) . In the case of D=f(c), if we apply x u t by the initial boundary condition, it will be the problem of Boltzmann-Matano analysis, and x will be also x t . 3. (a) 0 1 1 ( ) 2 B B c B c D c xdc dc t dx   6 2 . 0 7 1 0 t s 0 xdc defines the plane x=0. By graphical analysis, x=0 is found to be at the slice #25.

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10 15 20 25 30 35 40 45 50 10 20 30 40 50 a/o Ni Slice No.
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