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# HW3 - Louisiana State University Mechanical Engineering...

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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 [111] 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 =[110] , E b =[100] , and E b =[111] for the (a) bcc and (b) fcc metal structure. (c) Which dislocations do you expect to be more stable in each structure?
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