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# Solution1 - Materials Science and Engineering 206/196...

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Materials Science and Engineering 206 /196 Prof. W.D. Nix Imperfections in Crystalline Solids Spring 2008 Homework Assignment #1 SOLUTIONS Problem 2 Diamond cubic structure can be looked as FCC structure (red) plus 4 tetrahedral-site atoms (blue) as shown in fig. 1. Since there are totally 8 tetrahedral sites in one unit cell of FCC structure, the other 4 empty tetrahedral sites are the interstitial sites. It is obvious that the size of the 4 empty interstitial sites is just same as Si atoms, i.e., r interstitial = r si . Furthermore, for FCC structure, there are totally 4 octahedral sites. Let’s consider the same positions in diamond cubic structure. If you put one atom in one octahedral site, for example, (1, 0, ½), one of the nearest atoms is just the blue atom at (3/4, ¼, ¼). Thus, the distance between these two atoms is just √3 /4 , equal to the distance between one blue atom and one nearby red atom. Therefore, r interstitial = r si . Fig. 1 Diamond cubic structure. Here blue atoms and red atoms are the same element, but they

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Solution1 - Materials Science and Engineering 206/196...

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