MSE_2610_HW_6_solutions - MSE 2610 Introduction to the...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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 = = = + × = = = ⎡− =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

MSE_2610_HW_6_solutions - MSE 2610 Introduction to the...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online