E4511ps3-txt

E4511ps3-txt - Engineering 45 The Structure and Properties...

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page 1 Engineering 45 The Structure and Properties of Materials Spring, 2011 Problem Set No. 3 Problem 1: (a) Draw the face-centered cubic structure. Find the positions of the atoms, and the positions of the octahedral and tetrahedral voids within the structure. How many lattice sites, octahedral and tetrahedral voids are contained in a cell? (b) Let a material have the fcc structure, and consist of spherical atoms that just touch one another. What is the radius of the largest sphere that will fit inside an octahe- dral void without distorting the structure? What is the radius of the largest sphere that will fit in a tetrahedral void without distortion? [Hint: the geometry of the tetrahedral void is much easier to treat if you first show that the center of the void lies at the center of a cube that is 1/8 the size of the fcc unit cell.] Problem 2: Show that the hcp structure also has precisely two tetrahedral voids and one octahedral void per atom and that these have exactly the same size (relative to the atom
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E4511ps3-txt - Engineering 45 The Structure and Properties...

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