hs02201f10 - EMSE 201 Introduction to Materials Science...

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EMSE 201 – Introduction to Materials Science & Engineering Fall 2010 Case Western Reserve University Case School of Engineering Solution to Homework #2 Explain how answers were obtained. Give appropriate units for all numerical answers. 1) a) (6 points) In the style of C&R Figures 3.26 and 3.27, sketch the following planes in the rock salt (also known as the halite or sodium chloride) structure. Clearly distinguish and identify the two types of atoms in each sketch. Solution Note that the origin can be placed on either the large ions (as shown here) or the small atoms; in the latter case, the positions of the large and small ions would be switched. Either way is equally correct. (each sketch: 2 pts ) b) (3 points) Of the three planes sketched in part a, identify which planes would be considered nonpolar planes (i.e., containing balanced charge from cations and anions) and which planes would be considered polar planes (i.e., containing unbalanced charge). Solution On the {100} planes, there are four large corner ions contained in the area shown, (equal to a 2 where a is the cell edge length), and one large interior ion, so (4 × ) + (1 × 1) = 2 net large ions; whereas there are four small ions on edges, so (4 × ) = 2 net small ions, exactly balancing the large ions. Therefore the {100} planes are non-polar. ( 1 pt ) On the {110} planes, there are four large corner ions contained in the area shown, (equal to 2 a 2 ), and two large ions on edges, so (4 × ) + (2 × ) = 2 net large ions; whereas there are two small ions on edges and one on the interior, so (2 × ) + (1 × 1) = 2 net small ions, exactly balancing the large ions. Therefore the
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hs02201f10 - EMSE 201 Introduction to Materials Science...

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