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Homework_2 - Introduction To Materials Science Chapter 1...

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Unformatted text preview: Introduction To Materials Science, Chapter 1, Introduction Composites Thin crystalline platelets grown fromCr,lut-on ,- Mo ihs voldhis crystal structure so !i Fe cha na f e t back and forth: chain-folded model Spring 2007 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 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 1-14 Chapter 12 sections 1-4 Chater 14 sections 1-4 1. Linear and Planar Densities a. Determine the planar density and packing fraction for FCC nickel in the (100), (110) and (111) planes. Which, if any, of these planes is close packed. b. Sketch a portion of the (110) atomic plane in the bcc structure. The portion that you are to sketch must extend from 1,0,0 (lower left) to -1,2,0 (lower right) to -1,2,2 (upper right) to 1,0,2 (upper left). c. Represent the atoms as contacting circles and show the [1 1 1 ]direction and the [ 1 10 ] direction. [The atoms should lie in the plane of the paper, and your sketch must be scaled correctly.] 2. Ceramic Structure Draw the unit cells of cesium chloride, sodium chloride, and zinc-blende crystal structures. Using the ionic radii, establish the anticipated crystal structures for the following compounds (assuming they are cubic) and determine the lattice parameter (i.e. the size of the cubic unit cell) in each case. i) MgO iii) CsCl ii) NaCl iv) LiI Spring 2007 Engineering Material 3. Imperfection in Solids In terms of the metal atom radius R, determine radius r of the largest sphere that could fit into an 1/2 0 1/2 interstitial site in a bcc metal without pushing the metal atoms apart. For this type of problem, (and only for this type of problem), assume that the metal atoms are contacting spheres. [1 points] Energy x A B Figure 1 a. Explain in your own words the significance of line defects and point defects to the properties of materials [2 points] b. The number of vacancies in some hypothetical metal increases by a factor of five when the temperature is increased from 1000˚K to 1120˚K. Compute the energy for vacancy formation assuming that the density of the metal remains the same over this temperature range. [2 points] c. The interstitial site for dissolving a carbon in α-Fe is shown in the figure. 1. How much oversize is the C atom in α-Fe. 2. Consider now the case for interstitial solution of Carbon in high-temperature fcc structure of γ-Fe. The largest interstitial site is a [1/2 0 1] type 3. Sketch this interstitial solution in a manner similar to the figure below [1 point] 4. Determine by how much the C atom in γ-Fe is oversize [3 points] (Note the atomic radius for fcc iron is 0.127 nm) ...
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