MSE_2610_HW_6_solutions

# MSE_2610_HW_6_solutions - MSE 2610 Introduction to the...

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MSE 2610 Introduction to the Mechanical Properties of Materials Fall 2008 Homework Assignment #6 Due: 30 October 2008 1.) Describe two diffusion mechanisms; include a simple schematic to illustrate both diffusion mechanisms. Answer the following about hypothetical diffusivity constants: Vacancy Mechanism Interstitial Mechanism Diffusing atom a. If the diffusivity of copper in aluminum is equal to 4.74x10 -13 m 2 /s at 600 o C and 4.20x10 -14 m 2 /s at 500 o C, estimate the empirical constants D o and Q for this system. s / m 10 x 09 . 6 D ) K 873 )( K / eV 10 x 62 . 8 ( 41 . 1 exp D s / m 10 x 74 . 4 eV 41 . 1 Q ) K 873 )( K / eV 10 x 62 . 8 ( Q ) K 773 )( K / eV 10 x 62 . 8 ( Q exp ) s / m 10 x 74 . 4 ( s / m 10 x 2 . 4 ) K 773 )( K / eV 10 x 62 . 8 ( Q exp D s / m 10 x 20 . 4 ) K 873 )( K / eV 10 x 62 . 8 ( Q exp D s / m 10 x 74 . 4 kT Q exp D D 2 5 o 5 o 2 13 5 5 2 13 2 14 5 o 2 14 5 o 2 13 o = = = + × = = = ⎡− =

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b. This is diffusion data collected for the self-diffusion of aluminum: Temperature (K) Diffusion Constant (m 2 /s) 550 1.53x10 -18 640 2.00 x10 -16 690 1.06 x10 -15 720 2.84 x10 -15 800 3.31 x10 -14 900 3.55 x10 -13 Use linear regression to estimate the empirical constants D o and Q for the self diffusion of aluminum. Diffusion Coefficient for Self-Diffusion in Al y = -17326x - 9.3659 R 2 = 0.9987 -45 -40 -35 -30 -25 0.001 0.0012 0.0014 0.0016 0.0018 0.002 1/T (K -1 ) ln(D), Diffusion Coefficent (m 2 /s) eV 49 . 1 ) K / eV 10 62 . 8 ( ) K 17133 ( k m Q s / m 10 56 . 8 ) 37 . 9 exp( ) b exp( D 5 2 5 o = × × = × = × = = = 2.) A thin film of Co was deposited on the end of a long cylinder of Fe 3 O 4 . Afterwards the cylinder was annealed for 20 hours and the Co concentration measured in sections of the cylinder. The data is presented below, normalized by M (total amount of cobalt). Calculate the diffusion coefficient of Co in Fe
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## This note was uploaded on 12/24/2008 for the course MSE 261 taught by Professor Sass during the Fall '06 term at Cornell.

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MSE_2610_HW_6_solutions - MSE 2610 Introduction to the...

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