Of materials science and engiineeriing of virgi24ia

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Unformatted text preview: ials Science and Engiineeriing of Virgi24ia, Dept. of Materials Science and Engineering U n v e r s ty n 9 Reading Assignments Chapters 1, 2 Chapter 3 sections 1-14 Chapter 12 sections 1-4 Chater 14 sections 1-4 Problem 3 a. We need to consider two limiting cases when calculating the interstitial site radius, first that it fits in plane (001) and the second that it first in plane (002). Case of plane (001) In this case the condition is 2 rinterstitial + 2 R = 2a noting that for a bcc lattice a= 4R 3 we get after some manipulation: ⎛2 2 ⎞ rinterstitial = ⎜ − 1⎟ R ⎜ ⎟ ⎝3 ⎠ Spring 2005 Engineering Material Case of plane (002) In this case the geometric condition becomes 2 rinterstitial + 2 R = a which yields Energy x A B rinterstitial = 1 ⎛ 4 R⎞ ⎜ ⎟−R 2 ⎝ 3⎠ ⎛2 ⎞ =⎜ − 1⎟ R ⎝3 ⎠ which is obviously the more constraining cond...
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