Homework5-solutions - MAT 33 Fall 2007 Due Homework#5...

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MAT 33 – Fall 2007 Homework #5 - Solutions Due: 10/15/07 1.) The diffusivity of copper atoms in the aluminum lattice is 7.5 x10 -13 m 2 /s at 600 o C and 2.50 x 10 -15 m 2 /s at 400 o C. Calculate the activation energy in kJ/mol for this case in this temperature. D (m 2 /s) T (K) 2.5 x 10 -15 673 7.5 x10 -13 873 Using D = D o exp - Q d RT we set up two simultaneous equations with Q d and D o as unknowns. Solving for Q d and eliminating D o in terms of temperatures T 1 and T 2 and D 1 and D 2 we get Q d = - R ln D 1 - ln D 2 1 T 1 - 1 T 2 = - 8.31J/mol-K [ ln (2.5x10 -15 ) – ln(7.5 x10 -13 ) ] [1/673 – 1/873] = 139,300 J/mol = 139.3kJ/mol 2.) For the diffusion data given below, answer the following questions; a.) Which process has the higher activation energy: i.) the diffusion of C in BCC Fe or ii.) the diffusion of Fe in BCC Fe. What is the graphical basis of your argument? b.) From the limited data here would you expect that the grain boundaries in a polycrystal constitute overall a faster or a slower diffusive path? Why?
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  • Fall '07
  • keith
  • Atomic diffusion, carbon content, BCC Fe

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