Homework5-solutions

Homework5-solutions - MAT 33 Fall 2007 Due: 10/15/07...

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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? c.) What is the activation energy for the diffusion of Cu in Cu?
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This note was uploaded on 02/09/2008 for the course MAT 33 taught by Professor Keith during the Fall '07 term at Lehigh University .

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Homework5-solutions - MAT 33 Fall 2007 Due: 10/15/07...

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