Louisiana State University Mechanical Engineering Department Professor Meletis ME 2733 Fall 2004 Materials of Engineering Homework Assignment #3 (due: in class Friday, October 1, 2004) 1. A material consisting of two metals with two different structures, BCC and FCC structures, is studied by x-ray diffraction. The wavelength of the x-ray used is λ = 0.1542 nm. The diffraction pattern reveals diffraction peaks at the following 2 θ angles: 40.64 ˚ , 43.2 ˚ , 50.5 ˚ , 58.82 ˚ , 73.94 ˚ , 74.2 ˚ . Determine which peaks belong to each one structure and the lattice parameter of each material. 2. Calculate the linear atomic density in the  direction of (a) Cu and (b) Cr. 3. The energy necessary to generate a dislocation is proportional to the square of the length of the Burgers vector, ⏐ b ⏐ 2 . This means that the most stable (lowest energy) dislocations have the minimum length, ⏐ b ⏐ . Calculate the dislocation energies E b = , E b = , and E b = for the (a) bcc and (b) fcc metal structure. (c) Which dislocations do you expect to be more
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