MSE_2610_HW_2_solutions - MSE 2610 Introduction to the...

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MSE 2610 Introduction to the Mechanical Properties of Materials Fall 2008 Homework Solutions #2 DUE: 18 September 2008 1.) Sketch the planes and directions listed below. Be sure to label your axes. a.) Planes in a cubic crystal: (011), (111), (212) b.) Directions in a cubic crystal: [111] , [214], [103] c.) Planes in a hexagonal crystal: (1011), (1010) Not Graded d.) Directions in a hexagonal crystal: [1001], [0112] Not Graded 2.) a.) Sketch the simple, face-centered, and body-centered cubic unit cells Simple Cubic Body-Centered Cubic Face-Centered Cubic b.) Calculate the atomic packing factor of the three cubic Bravais lattices - Simple Cubic a r 2 = () 523 . 0 6 π r 2 r π 3 / 4 a r π 3 / 4 f 3 3 3 3 SC = = = = - Body-Centered Cubic 3 a r 4 = () 680 . 0 8 3 π r 3 / 4 r π 3 / 4 a r π 3 / 4 2 f 3 3 3 3 BCC = = = = - Face-Centered Cubic 2 a r 4 = () 740 . 0 6 2 π r 2 / 4 r π 3 / 4 a r π 3 / 4 4 f 3 3 3 3 FCC = = = = c.) Are any cubic lattices close-packed? If so, which families of planes and directions are close-packed?
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- The FCC lattice is a close-packed structure. In FCC, the {111} family of planes are close- packed planes, and the <110> family of directions are close-packed directions. d.) Calculate the theoretical density of aluminum based on the crystal structure and molar
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MSE_2610_HW_2_solutions - MSE 2610 Introduction to the...

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