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MatSci%20201%20HW2%20Solutions%202008 - MatSci 201...

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MatSci 201: Introduction to Materials Homework #2 Solutions 65 points total 1. (10 points) The packing factor for a body-centered cubic (BCC) structure is 68% when all of the atoms are of equivalent size. Later in the quarter, we will study ceramic materials where ions are of different sizes. CsCl, for example, looks body-centered cubic, except that the body center atom is different from the eight corner atoms. Based upon the table of ionic radii in your course notes (Week 1, page 23), determine if there is a higher or lower packing factor in CsCl than the BCC’s 68%. Show all steps in your calculation. In the BCC structure the center and corner atoms touch one another along the cube diagonal. Therefore in the ionic structure, the unit cell length a and the atomic radius R are related through a = 2 R Cs + + 2 R Cl 3 = 2(0.169) + 2(0.181) 3 = 0.404 nm . The unit cell volume is a 3 or 0.066 nm 3 . The unit cell contains one Cs ion and one Cl ion – one ion in the center and 8 (1/8) in the corners.
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