Assignment3_solution

# Assignment3_solution - Assignment#3 Solutions ME264...

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1 Assignment #3 Solutions ME264 Materials Science for Mechanical Engineering Spring 2009 Due Date: 4 March 2009 (5 pts) 1. (1pt) (a) Calculate the density of an f.c.c. packing of spheres of unit density. (b) If these same spheres are packed to form a glassy structure, the arrangement is called “dense random packing” and has a density of 0.636. If crystalline f.c.c. nickel has a density of 8.90 Mg m -3 , calculate the density of glassy nickel. Solution: (a) Let the spheres have a diameter of 1. Then the unit cell has an edge length 2 , and a volume 2 2 . It contains 4 atoms, with a total volume 4 6 π . Hence density, ρ , is given by ( ) ( ) 4 0.740 6 2 2 ρ = = (b) Glassy nickel is less dense than crystalline nickel by the factor 0.636 / 0.740 . The density is therefore ( )( ) 3 8.90 0.636 / 0.740 7.65 Mg m - = 2. (2pts) (a) Sketch three-dimensional view of the unit cell of b.c.c. crystal, showing a (100) plane, a (110) plane, a (111) plane and a (210) plane. (b)

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Assignment3_solution - Assignment#3 Solutions ME264...

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