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King Fahd University of Petroleum & Minerals Mechanical Engineering Department ME 205: Materials Science Semester (151) Homework # _2_ Assigned on: 30/09/2015 Due date: 07/10/2015 (Please, use this page as a cover page) Name: ________________________ _____________________ ID#: Section #: _________ Problems Marks Grades 1 10 2 15 3 10 4 10 5 15 6 20 7 20 Total 100 1 1) Show that the atomic packing factor for BCC is 0.68. 2 2) Show that the atomic packing factor for HCP is 0.74. 3 3) Calculate the radius of a vanadium atom, given that V has a BCC crystal structure, a density of 5.96 g/cm3, and an atomic weight of 50.9 g/mol. 4 4) Iodine has an orthorhombic unit cell for which the a, b, and c lattice parameters are 0.481, 0.720, and 0.981 nm, respectively. (a) If the atomic packing factor and atomic radius are 0.547 and 0.177 nm, respectively, determinethe number of atoms in each unit cell. (b) The atomic weight of iodine is 126.91 g/mol; compute its theoretical density. 5 5) Titanium has an HCP unit cell for which the ratio of the lattice parameters c/a is 1.58. If the radius of the Ti atom is 0.1442 nm, (a) determine the unit cell volume, and (b) calculate the density of Ti and compare it with the literature value. 6) (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R. (b) Compute and compare linear density values for these same two directions for tungsten. 6 7 7) (a) Derive planar density expressions for FCC (100) and (111) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for nickel. 8 9 10