Unformatted text preview: Introduction To Materials Science, Chapter 1, Introduction Composites Thin crystalline platelets grown fromCr,luton , Mo ihs voldhis crystal structure so !i Fe cha na f e t back and forth: chainfolded model Spring 2005 Engineering Material Polyethylene
Polymer composite materials: reinforcing glass fibers in a polymer matrix. University of Virginia, Dept. of Materials Science and Engineering Homework #2
18 (Solution) The average chain length is much greater than the thickness of the crystallite
University of Virginia, Dept. of Materials 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 114 Chapter 12 sections 14 Chater 14 sections 14 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 condition, thus ⎛2 ⎞ rinterstitial = ⎜ − 1⎟ R ⎝3 ⎠
b. c. Let NV1 = Nv at 1120˚K and NV2 = Nv at 1000˚K Engineering Material ⎜−⎟ − ⎜ R ⎜T T ⎟⎟ N V1 Ne = 5= = e⎝ ⎝ 1 2 ⎠ ⎠ ⎛Q⎞ ⎜− V ⎟ NV 2 ⎜ ⎟ Ne⎝ RT2 ⎠ R ln 5 (8.31 J / mol˚ K ) ln 5 ⇒ QV = − 1 1 = − = 116300 J / mol 1 1 − − T1 T2 1120 1000 ⎛Q ⎜− V ⎜ RT ⎝ 1 ⎞ ⎟ ⎟ ⎠ ⎛Q⎛ 1 V ⎜ ⎞ 1 ⎞⎟ Problem 4
a. ⎛2 ⎞ rinterstital = ⎜ − 1⎟ R ⎝3 ⎠
with R = 0.124 nm we get rinterstital=4 .0 1 = 0.077nm ⇒ rC a r b o n 0.077 = rinterstital 0.0192 this explains the low solubility of Carbon in αFe b. c. 4R = 2 R + 2rinterstitial 2 2R ⇒ rinterstitial = − R = ( 2 − 1) R = 0.0526nm 2 r 0.77 ⇒ Carbon = = 1.46 rinterstitial 0.0526 a= ...
View
Full Document
 Summer '07
 MarwanDarwiche
 Materials Science, Crystal, Composite material, Dept. of Materials Science and Engineering

Click to edit the document details